Manchester City returned to the Premier League summit for the first time since January with a 3-2 win at Everton on Saturday that left them six points from a second title in three seasons.
Edin Dzeko's double put them in charge at Goodison Park after Sergio Aguero fashioned an equaliser as they recovered from a superb early Ross Barkley goal for the home side.
Romelu Lukaku gave fifth-placed Everton hope with a 65th-minute effort but City hung on to move above Liverpool with a far superior goal difference and two games left.
Both sides have 80 points with Chelsea, who can go top with a win over Norwich City on Sunday, on 78 with two to play.
Liverpool visit Crystal Palace in their penultimate game on Monday before finishing at home to Newcastle United while City host Aston Villa on Wednesday and West Ham United next Sunday.
Cardiff and Fulham relegated, Sunderland near survival
The trap door slammed shut on Cardiff City and Fulham as crushing away defeats condemned both clubs to relegation from the Premier League on Saturday while rejuvenated Sunderland moved to the brink of survival.
Sunderland's impressive burst of form continued as they earned a 1-0 win at Manchester United - a result that took them beyond the reach of Cardiff, 3-0 losers at Newcastle United, and Fulham who were crushed 4-1 at Stoke City.
Gus Poyet's side's third consecutive victory, clinched by Sebastian Larsson's well-worked winner on the half hour, took them to 35 points in 17th place with two games remaining while Cardiff (30) and Fulham (31) only have one left.
Sunderland will be guaranteed survival if Norwich City lose away at Chelsea on Sunday.
"I said a long time ago that we would fight to the end, and what a game of football we played today," Poyet, whose side reached the League Cup final this season, told the BBC.
"I don't know how many records have changed this season, we have been down there all season but if we win and stay up it's an incredible season."
"I hope my old team Chelsea give me a hand tomorrow," added the Uruguayan.
Shola Ameobi, Loic Remy and Steven Taylor all scored for Newcastle to make Cardiff's return to the top flight for the first time since 1962 a brief one.
While it was Cardiff who went down, however, the home fans were also restless with a protest during the match against manager Alan Pardew and owner Mike Ashley.
A 69th minute "walk-out" was planned and while many did vacate their seats it was not the thousands predicted.
Peter Odemwingie, Marko Arnautovic, Oussama Assaidi and Jonathan Walters all scored for Stoke as Fulham's 13-year stay in the Premier League came to an abrupt end.
Felix Magath, Fulham's third manager this season, suffered the first relegation in his long coaching career.
"There was no reason for that performance - it's the worst game since I've been here," Magath, whose side threw away 2-0 lead against Hull City last weekend, told the BBC.
"I didn't expect it. We were fighting against relegation. I told the team, today was a great chance but we never took the chance."
WEST HAM WIN
In an early kickoff West Ham United guaranteed their safety, reaching 40 points with a 2-0 win over 10-man Tottenham Hotspur - their third victory over their London rivals this season.
An own goal by Spurs striker Harry Kane and Stewart Downing's free kick put West Ham in control before halftime after Tottenham defender Younes Kaboul was red-carded for bundling over Downing who was racing towards goal.
Southampton won 1-0 at Swansea City with Rickie Lambert's stoppage time winner while Aston Villa, who began the day not mathematically safe, beat FA Cup finalists Hull City 3-1.
Attention turns to the title race later on Saturday when Manchester City take on fifth-placed Everton knowing a victory would put them top of the table, ahead of Liverpool, who play Crystal Palace on Monday, on goal difference.
Sunderland's revival was expected to come under severe scrutiny against a United side buoyed by Ryan Giggs' promotion to caretaker coach in the wake of David Moyes's sacking.
However, the Giggs effect did not materialise as it did against Norwich last weekend and Sunderland deservedly grabbed a first win at Old Trafford since 1968 when Larsson swept in a cross from Connor Wickham.
The visitors also hit the woodwork twice through Fabio Borini and Emanuele Giaccherini.
"I feel flat. The players were flat and I don't know why. Credit to Sunderland they are in good form, and they created the best chances. We lacked that bit of quality in the final third," Giggs said after United's 12th league defeat of the season.
Defeat left United in seventh spot, six points behind Tottenham and while they have a game extra to play they now look like missing out on Europa League football next season when Dutchman Louis van Gaal is favourite to be in charge.
Image: Edin Dzeko
Photograph: Laurence Griffiths/Getty Images
