LONDON (Reuters) - Edin Dzeko's double at Everton helped Manchester City clear the biggest obstacle blocking their route to a second English title in three years on Saturday but Cardiff City and Fulham fell through the relegation trapdoor.
Bosnian striker Dzeko scored either side of halftime at Goodison Park as City won 3-2 to return to the summit for the first time since January and home wins against Aston Villa and West Ham United next week would almost certainly seal the title.
Everton, whose defeat means Arsenal will finish in the top four and qualify for the Champions League, led early on with a gem from Ross Barkley but Argentina striker Sergio Aguero equalised and Dzeko put the visitors in command.
Romelu Lukaku ensured a nervy finale with a second for the home side but City, for whom keeper Joe Hart made several fine saves, hung on to move above Liverpool on goal difference.
Both sides have 80 points with two games to play while Chelsea are third on 78, also with two games to play beginning at home to relegation-haunted Norwich City on Sunday.
Liverpool play their penultimate game away to Crystal Palace on Monday with City, who boast a nine-goal superior goal difference, at home to Villa on Wednesday before next Sunday's finale to a gripping season.
"It was a really, really big step. To play here against Everton is difficult," City manager Manuel Pellegrini told Sky Sports. "We won and that is important.
"The pressure is maybe too high to play your best football. It is not easy to recover from a goal down but we did."
City's relief was in marked contrast to the emotions experienced by Cardiff and Fulham whose relegation was confirmed by a surprise 1-0 win for Sunderland at Manchester United.
Sebastian Larrson's first-half goal gave Sunderland their first win at Old Trafford since 1968 - 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 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 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 hope my old team Chelsea give me a hand tomorrow."
For United's caretaker manager Ryan Giggs it was a sobering afternoon after the high of his side's 4-0 win against Norwich last weekend in his first match in charge since taking over from David Moyes, who was sacked last week.
"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 seventh home league defeat of the season - their worst record since 1973-74 when they went down.
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.
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 and gave manager Felix Magath his first taste of relegation as a coach.
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.
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.
Man City were not at their best against an Everton side who have run out of steam of late but showed their mettle to claw out a hugely important victory.
They were stunned when Barkley curled a shot beyond Hart after 11 minutes but they were level soon afterwards when Aguero scored with a near-post shot shortly before hobbling off.
Dzeko's towering header gave City the lead in the 43rd minute and the tall striker stabbed in Samir Nasri's low cross early in the second half to give his side a cushion.
City retreated in the latter stages though and when Lukaku's diving header reduced the deficit in the 65th minute another twist in the title race looked possible.
Hart had to make one sharp save to deny Gerard Deulofeu but City held on to move into the final week of the season with a slender, but probably decisive, advantage.
(Reporting by Martyn Herman; editing by Josh Reich)