Bob McHugh and James McFadden scored as Motherwell eased past 10-man Livingston and into Thursday's Scottish League Cup quarter-final draw.
McHugh headed in from close range following Lionel Ainsworth's corner.
Livingston had Jason Talbot sent off for a challenge on Stevie Hammell before McFadden doubled 'Well's lead in style with a wonderful back-heel flick.
The hosts pulled one back late on when Danny Denholm bundled in at a corner but Motherwell held out for the win.
It means Stuart McCall's men get a stage further in the competition than last season, when they were knocked out in the third round by Rangers.
This was Livingston's first defeat under new manager John McGlynn and they can now focus on lifting themselves off the bottom of the Scottish Championship.
McFadden started up front after finding himself coming off the bench in Sunday's 2-2 draw with Dundee United and McCall will hope this first goal of the season for the Scotland international can be followed by more.
McHugh was on hand to convert Simon Ramsden's flick from the set piece to put the visitors ahead but few chances for either side followed.
Motherwell enjoyed decent possession and Livingston escaped a penalty claim before the break when Coll Donaldson came through the back of McFadden with a sliding tackle.
Donaldson had another let-off after the restart when he dallied on the ball inside his box and then slipped under pressure from Stuart Carswell.
The midfielder played the ball across for McFadden but a timely challenge prevented the former Everton forward from getting a clean strike.
Livingston went close on the hour mark when Andrew Barrowman met Callum Fordyce's cross with a powerful header.
Referee Brian Colvin deemed Talbot's sliding tackle on Hammell reckless even though the Livi man appeared to win the ball.
Motherwell moved quickly to press home their advantage and doubled their lead with a vintage piece of skill by McFadden.
Another McFadden back-heel set up a string of shooting chances but Darrren Jamieson made a triple save from John Sutton, Ramsden and the Scotland forward.
Denholm's goal set up an anxious few minutes for the visitors at the end but overall it was a deserved win for 'Well.
Motherwell boss Stuart McCall: "I thought Livingston were terrific. They did not cause us many problems but I thought the spirit was good.
"It was only when they went down to 10 men did we start to create more chances. We deserved to win the game but I thought they were a credit to John because he puts so much work in to what he does whether he is at Raith Rovers or Hearts and he'll get them going I'm sure.
"We had good passages of play but I'm disappointed to lose a goal at the end. Over the piece we're pleased to be through."
Livingston manager John McGlynn: "I thought we played football. It was very nice of Stuart McCall to give us compliments because I've got the greatest respect for him and Motherwell are an excellent side.
"It's hard enough playing Motherwell with 11 never mind 10 so it was difficult after the sending off.
"I haven't seen it again but it is high up the pitch and I don't see the reason for going into the tackle.
"We could have done something else rather than go to ground as it gave Motherwell more breathing space on the pitch and they created one or two chances after that."