Cardiff City received a boost as Premier League relegation rivals Brighton lost 1-0 at Tottenham Hotspur.
But Southampton went six points clear of the Bluebirds as they drew 1-1 at Watford.
Cardiff sit 18th, three points behind Brighton, with the Saints three points above the Seagulls.
If they go down, Cardiff could renew rivalries with Swansea City in the Championship - although Graham Potter's team can still make the play-offs.
Nine more points are available to the Bluebirds, who complete their season with games against Fulham, Crystal Palace and Manchester United.
A 1-0 win at Ipswich ended the Swans' worst Championship away run and revived their chances of a late push for the top six.
Swansea are five points outside the play-offs with three games to play.
Hull City visit the Liberty Stadium on Saturday, 27 April followed by games against Derby County and Blackburn Rovers.
Swansea will need to finish their season in style and hope their four competitors in the race for the last available play-off place slip up.
Managers on the run-ins
|Battle for Premier League survival|
|Cardiff fixtures||Brighton fixtures||Southampton fixtures|
|Fulham (A)||Newcastle (H)||Bournemouth (H)|
|Crystal Palace (H)||Arsenal (A)||West Ham (A)|
|Man Utd (A)||Man City (H)||Huddersfield (H)|
Neil Warnock, Cardiff City: "Brighton are going to play Newcastle, who have nothing to play for, so they will be looking at that game.
"We have got to play Fulham and Palace at home and Manchester United and do the best we can - that's all we can do.
"I would imagine we have got to get two wins and a draw. Anything is possible the way we are playing.
"We are more comfortable now in the Premier League than we were at the start of the season, but it's a stiff task."
|Race for the Championship play-offs|
|Derby (6th, 67 points)||Boro (7th, 67)||Bristol City (8th, 66)||Sheff Wed (9th, 63)||Swansea (10th, 62)|
|Bristol City (A)||Reading (H)||Derby (H)||Preston (A)||Hull (H)|
|Swansea (A)||Millwall (A)||Derby (H)|
|West Brom (H)||Rotherham (A)||Hull (A)||QPR (H)||Blackburn (A)|
Graham Potter, Swansea City: "The fact that we are going into the last week of the season and it's still a possibility, however slight it is, says a lot for the group.
"We have had to keep going at times - we have had to come back from setbacks.
"We are in good form at home. We have to win our next two games and then we'll see.
"71 points might not be enough - it's out of our hands. But we have a young team who need every opportunity to get experience and learn so we will focus on the next match and try to win."
Likelihood of a derby?
Cardiff and Swansea last went head to head in 2013-14, a campaign which saw the Bluebirds relegated from the Premier League.
If the bookmakers are to believed, Wales' top two clubs will be reunited next season - in the Championship.
Brighton's run-in looks very demanding - the Newcastle game aside, perhaps - but the bookies believe Chris Hughton's team will survive, with Cardiff odds-on to go down.
However, Warnock's men will have high hopes should they back up their recent away win at Brighton with another travelling triumph at Fulham.
In the Championship, where Norwich and Sheffield United are firm favourites for automatic promotion, Leeds and Aston Villa are the two sides most fancied in the play-offs, ahead of West Brom.
Derby, Bristol City and Middlesbrough are all considered more likely to make it to the Premier League than Swansea, who are distant 100-1 shots at this stage.
Then again, Swansea would have momentum on their side should they scrape into the top six by winning their three remaining regular-season games.
They would not be the first team to make a spectacular, springtime push for promotion, even if the feeling is Potter's side have left it a little late.
All to play for in Wales
Cardiff and Swansea are not the only Welsh clubs with all to play for at this late stage in 2018-19.
Newport County are one of a host of clubs scrapping it out for a place in the League Two play-offs.
Michael Flynn's team are currently 11th, two points outside the top six, but have a game hand on every club above them.
Unbeaten in seven matches, the Exiles host champions Lincoln this weekend before facing Oldham (h) and Morecambe (a).
And in the National League, Wrexham are in the play-offs for the first time in six years as they look to return to the EFL.
Wrexham face Harrogate in their final regular-season game this Saturday with the play-offs to come next week.