That's all folks. Thanks for your company tonight and look out for some fine goals when we publish the highlights from both games on the website later. Join us again on Friday for the Lanarkshire derby as Hamilton Academical host relegation-haunted Motherwell.
"We could have made it easier for ourselves, but the important thing was getting three points.
"The sending off changes the game, but we had opportunities to finish it before that.
"It was not easy out there and our decisions could have been better, but it was a good response after Saturday.
"We are down to the last two games and it keeps it ticking over and we'll see what happens in the play-offs."
"I am delighted with the work rate and fitness of the guys and I think the game changed with the sending off.
"I am not for hard luck stories and we march on to Raith Rovers on Saturday.
"If we go and get the six points, I think we'll be in the division again next season."
BBC Radio Scotland pundit Murdo MacLeod was at the match at Almondvale tonight and thinks Livingston will still get enough points in their final two games to avoid the automatic relegation spot. He also thinks Hibs have the easier run-in than Rangers and that this will put pressure on the Ibrox side in the race to finish second in the Championship.
"I thought our final ball let us down, but we had a good disciplined performance.
"Two set-pieces done for us, but I am pleased with the players.
"You can see at the end that my players were knackered because Celtic are a quality side and play the ball about so well.
"But I thought we handled it well tonight and overall this season I'm proud of the players."
Celtic boss Ronny Deila also pointed out that he was delighted to hand 17-year-old Kieran Tierney his debut as a late sub for Emilio Izaguirre at left-back and suggested he is "a big talent".
"That was a little bit naive of us to concede a goal so late.
"But we controlled the game until late on and we scored good goals.
"That is a good effort to come back from 120 minutes on Sunday.
"We won comfortably in the end and put ourselves in a good position and the title's getting closer and closer."
Paul Black: "10 goals for VVD this season is a great return for a centre back. The lad is phenomenal."
"Celtic by far deserve their victory. Craig Gordon was not really tested on too many occasions. The strange thing was Dundee actually managed to beat him. Their possession was hopeless and they managed to dig out a respective scoreline even though it was a canter for Celtic."
Hibs move to within a point of second-top Rangers in the Championship with only two games remaining as they battle for positions in the promotion play-offs. Livingston miss a chance to move off the bottom on goal difference ahead of Alloa Athletic.
Dundee remain four points adrift of St Johnstone in sixth place.
Celtic move eight points clear of Aberdeen at the top of the Premiership once more and they hardly needed to break sweat.
Dundee are living dangerously as they hand another free-kick outside the penalty box. However, this time Virgil van Dijk fires straight at the goalkeeper.
Three minutes of stoppage time for Dundee to save a point.
The first time that Dundee get behind the Celtic defence and they are suddenly back in the game. Luka Tankulic plays a superb ball behind Nir Biton and Paul McGinn's low cross is swept home by Jim McAlister.
At last a clear-cut change for Dundee, but Luka Tankulic blasts well over the bar from 12 yards.
It's a third for Hibs. Dominique Malonga dances his way towards the six-yard box then slips a shot past Darren Jamieson.
Fraser Fyvie picks out Liam Fontaine with a chip into the Livi box and Declan Gallagher sweeps off the line after goalkeeper Darren Jamieson is beaten by the header.
BBC Sport Scotland
"Just over 15 minutes to go in Livingston. Hibs are comfortable in possession and the hosts, who are a man down, are tiring."
Celtic bring on Kris Commons and John Guidetti for James Forrest and Leigh Griffiths. Two additional scoring threats for the visitors, so it is not getting easier for the hosts, who have not yet seriously threatened Celtic goalkeeper Craig Gordon.
"It hasn't been an exciting game, but you have to illuminated by the quality of the goals tonight."
Dundee centre-half James McPake is booked for a foul on Stuart Armstrong and Virgil van Dijk takes a couple of steps before powering a drive past the home goalkeeper. Almost a mirror image of the Dutch defender's goal on Sunday in the Scottish Cup sem-final against Inverness.
Hibs have a penalty and that seemed harsh on Livi. Kyle Jacobs appeared to win the ball in his challenge on Dylan McGeouch. However, the Hibs midfielder has his spot-kick beaten away by Darren Jamieson.
Dundee manager Paul Hartley sends on German forward Luka Tankulic in place of the ineffectual Alex Harris.
Jamie McGilchrist: "GMS scoring against Dundee. No United fan saw that coming."
Hannah Ross: "GMS is going become a future star for Scotland - no doubt."
It is still Celtic applying the pressure and Scott Bain has to punch clear at the back post before a Leigh Griffiths shot from 10 yards is beaten away by the goalkeeper.
There's that shot on goal for Dundee at last. James McPake thinks he is Virgil van Dijk for a few moments, breaking from defence and even putting in a wee dribble, but he slips as he tries to shoot and goalkeeper Craig Gordon saves easily.
Celtic midfielder Nir Biton has shown in recent weeks that he can give the bit of a welly and the Israeli curls a powerful drive wide from 25 yards. Up the hill too!
Dundee kick-off at Dens Park. Will they get a shot on target now that they are shooting down the hill?
BBC Sport Scotland
"The first half ended on a sour note for the hosts, who were already trailing when they lost Darren Cole to a second yellow card. Hibs looked good going forward in the first half and deservedly scored two goals, but Livi have fought their corner well and scored a superb equaliser."
Livi are down to 10 men. Former Rangers defender Darren Cole concedes a free-kick and receives a second yellow card.
The Dundee defence are caught sleeping as they expect the ball to run out for a goal kick. But Celtic scorer Gary Mackay-Steven doesn't give up on it and his low cross spells danger before being cleared. James Forrest is next to threaten for Celtic but shoots straight at goalkeeper Scott Bain from 15 yards.
"Dundee have got themselves back into the game. They lost their passing, their ability, their shape, after the goal, but they have realised they are only one behind."
Chris Martin: "What's the chances of Celtic getting a penalty from a Dundee handball that hit a Dee chest?
Gary Parkes: "SFA citing Meekings is farcical and he is getting used as a scapegoat for the incompetence of the officials."
Stuart Mitchell: "Does someone want to tell Cammy Renwick that Paton's red card wasn't rescinded?" I'll leave that honour to you, Stuart. Ta!
BBC Sport Scotland
"Half an hour in, the game has calmed down a little after that three-goal burst. There's a confidence about Hibs when they go forward, but that has been matched at times by the determination of Livi to make life difficult for the visiting defenders."
Dundee might be the ones unhappy at the officials this time as referee Calum Murray calls the action back for a free-kick after initially waving play on until Gary Mackay-Steven loses possession. Stuart Armstrong's free-kick is headed on by Virgil van Dijk and it's picked up by former Dundee United man Mackay-Steven speeding into the penalty box to fire into the top corner of the net.
While most of the sympathy on Twitter has been towards Celtic, it's a different matter on the BBC Sport Scotland Facebook page.
Robert Thain: "Give Celtic the points, they will only complain if they get beaten."
Scott Mcalpine: "Penalty lol"
Brian Doig: "That Dundee will have a lot more supporters tonight than usual!"
Toby Michaels: "Celtic to lose then complain to the SFA?"
Clare Crook: "LOL they arent talking about Sunday anymore, LOL good luck to Dundee."
Pe Dro: "1-0 Dundee. Clarkson late strike from close range."
David Adamson: "3-0." But to whom, David?
Leigh Griffiths fires into the side netting as Celtic begin to apply more pressure on the home defence.
The Celtic fans' cries for a penalty go unheard by the referee as James Forrest crumples in the box after Dundee goalkeeper Scott Bain fumbles a cross leading to some panic in the home six-yard area.
Fred McGrath: "Boerrigter given a retrospective red card at the start of the season. The rules apply to all teams."
george mcgrory: "Glad to hear Ronnie Deila has moved on from Meekings scandal. Now he's banned, he's not interested."
The first attempt on target at Dens Park comes from Celtic as Virgil van Dijk rises at the back post to meet a Stuart Armstrong corner, but the Dutch defender's looping header is easy for goalkeeper Scott Bain.
The skies are clear in West Lothian, but it's raining goals at Almondvale as Livi fail to clear their lines and Jason Cummings fires low into the net at the second attempt from 12 yards. Are the clouds gathering for the home side's hopes of avoiding relegation?
Livi are level as Myles Hippolyte, who scored with a superb free-kick last week against Rangers, superbly volleys home a long ball after it bounces over the head of Jordon Forster at the back post.
It is commendable that Dundee are trying to play the ball out of defence, but they are playing a dangerous game and have been in danger of handing chances to their opponents after losing possession close to their own goal.
Celtic winger Gary Mackay-Steven sends a volley a couple of feet over the bar after chesting the ball down skilfully after another corner was cleared to the edge of the penalty box.
Hibs get off to an ideal start. A lovely passing move ends with Dylan McGeouch slipping the ball through for midfield colleague Scott Robertson to guide the ball into the net.
It is Celtic's turn to win a corner, but Stuart Armstrong's cross doesn't get past the front post.
The first corner of the game is won by Dundee as Alex Harris plays it off Virgil van Dijk, but Celtic clear the danger.
BBC Sport Scotland
"At Almondvale, Hibernian have the chance to narrow the gap on second-place Rangers back to one point, but they will have to beat Livingston, who have the incentive of moving from bottom place. Livi are three points shy of Alloa Athletic but have a superior goal difference.
"Hibs had a disappointment at the weekend when they were knocked out of the Scottish Cup at the semi-final stage by Falkirk, but Alan Stubbs' side can still end the season on a high by earning promotion via the play-offs."
Celtic kick off flashing in the sunlight in their all-white change strip, while Dundee are in all blue.
We are nearing kick-off at both grounds. You can listen to commentary from Dens Park on BBC Radio Scotland 810MW, while the live pictures from Livingston are on BBC Alba.
At Livingston, Hibs are themselves hoping to get over Scottish Cup semi-final disappointment after losing 1-0 to Falkirk at Hampden on Saturday. The home side are still bottom, but they are on a run of five games without defeat and drew 1-1 with second-placed Rangers in their last outing.
At Dens Park, both sides are looking to bounce back after their unbeaten runs were ended on their last outings. Dundee were beaten 1-0 away to St Johnstone on 11 April and, since then of course, Celtic lost Sunday's Scottish Cup semi-final to Inverness Caledonian Thistle 3-2 after extra-time. Can Dundee benefit from the rest and will the visitors be mentally and physically vulnerable?
Cammy Renwick: "Why the fuss? Paton red card retrospectively rescinded, Meekings retrospectively issued."
Livingston: Jamieson, Donaldson, Gallacher, Cole, Fordyce, Kyle Jacobs, O'Brien, Pitman, Hippolyte, White, Mullen. Subs: Boulding, Walker, Beaumont, McKenna, Glen, Sekajja, Currie.
Hibernian: Oxley, Forster, Hanlon, Fontaine, Boyle, McGeouch, Robertson, Fyvie, Stevenson, El Alagui, Cummings. Subs: Craig, Stanton, Handling, Malonga, Dja Djedje, Cerny, Dunsmore.
Referee: Andrew Dallas
Dundee: Bain, Paul McGinn, Konrad, McPake, Dyer, Ferry, McAlister, Harris, Stephen McGinn, Stewart, Heffernan. Subs: Letheren, Davidson, Clarkson, Tankulic, Black, Wighton, Colquhoun.
Celtic: Gordon, Ambrose, van Dijk, Denayer, Izaguirre, Biton, Brown, Forrest, Armstrong, Mackay-Steven, Griffiths. Subs: Guidetti, Stokes, Scepovic, Commons, Zaluska, Fisher, Tierney.
Referee: Calum Murray
The three missing out for Celtic are right-back Adam Matthews and midfielders Stefan Johansen and Kris Commons, with Efe Ambrose, Gary Mackay-Steven and Stuart Armstrong start for the visitors.
Talking of changes, Paul Hartley has made three of his own. Midfielder Paul McGowan misses due to the curfew he is under following his recent court conviction. Striker David Clarkson and midfielder Iain Davidson drop to the bench, with James McPake, Alex Harris and Paul Heffernan coming in.
"We are looking to get three points, there is a lot to play for and we want to catch the teams in front of us.
"The changes they have made, they have pace and a very strong squad.
"We expected the changes to be made and I was right with my predictions.
"We have freshened things up and gone a bit more attacking and are looking to make a good game of it."
Ronny Deila has entered the debate over Josh Meekings' possible ban in the Scottish Cup final.
"It is not a problem for me if he was to play in the Cup final," said the Celtic boss.
"I don't think about it now. I have moved on and what happens now has nothing to do with Celtic."
At Livingston, Hibs are looking to narrow the gap on second-top Rangers to one point as they chase the best positions in the promotion play-offs, while the home side can move level with second-bottom Alloa Athletic on points and ahead on goal difference as they look to avoid relegation.
"Sunday was very difficult for us and exhausting for some of the players.
"We have made some changes because we have a very good squad.
"This is a huge game for us and we are up for it.
"Dundee are a team that want to play and attack."
Celtic have again been in the news today as the shrapnel that has followed Sunday's Scottish Cup semi-final defeat by Inverness Caledonian Thistle has continued to fall. Fifa's head of referees Jim Boyce says the Scottish FA should not be offering Caley Thistle's Josh Meekings a one-match ban, which would mean the defender would miss their final against Falkirk, and are setting a dangerous precedent.
Give us your thoughts about that, tonight's action or any other issues in Scottish football that are biting your ankles.
Tweet #bbcscotfootball or leave a message on the BBC Sport Scotland Facebook page.
At Dens Park, Celtic and Dundee both play their final game before the Premiership splits into two sections of six teams. A victory for Celtic and the Glasgow side will stretch their lead at the top of the table over Aberdeen to eight points with five games remaining. Meanwhile, now that they have secured their place in the top half, sixth-placed Dundee are hoping to narrow the gap with St Johnstone to one point and boost their outside hopes of qualifying for the Europa League.
Welcome to another night of hot action under the spring sunshine in Scottish football. The main event is in the Premiership, where Dundee host leaders Celtic, while there is also an important game in the Championship, with Hibernian visiting Livingston.