Cardiff and Fulham down. City go top
Sunderland made it three Premier League wins on the bounce with a remarkable 1-0 victory at Manchester United to condemn Cardiff and Fulham to the drop and keep their own survival hopes firmly alive.
Sebastian Larsson's goal was enough to inflict Ryan Giggs' first defeat as United interim player-manager and continue their miracle revival.
Sunderland's win sent Fulham and Cardiff down, who both suffered defeats on Saturday afternoon in their penultimate matches of the season to Stoke City and Newcastle United respectively.
Manchester City assumed pole position in the title race with a 3-2 win but Everton gave the conspiracy theories short shrift after Manuel Pellegrini's side endured a testing time at Goodison Park.
Anything other than a City victory would have handed the initiative back to Liverpool but three points put them top of the table on goal difference with Chelsea to play Sunday and the Reds a day later.
Everton, despite many fans claiming they would be happy to lose in order to help stop their near-neighbours' title bid, needed a win themselves to stay in the hunt for the Champions League but defeat handed fourth spot to Arsenal 24 hours before they play.
Having proved they would not be rolled over by taking the lead through a Ross Barkley wonder-strike and fighting back through Romelu Lukaku's header, Everton were ultimately left empty-handed as Edin Dzeko's brace and Sergio Aguero's 17th Premier League goal earned City the spoils and the advantage in the title fight.
Newcastle ended a run of six successive defeats by beating Cardiff 3-0, with the latter being relegated on their debut season in the Premier League.
The Magpies converted their early pressure into a goal as Shola Ameobi gave them the lead after 18 minutes from Moussa Sissoko's cross to the far post. It was Ameobi's second goal in as many games at St James' Park.
Newcastle manager Alan Pardew was back in the home dugout for the first time since Feb. 23 after serving a seven-game ban for head-butting Hull City's David Meyler.
A number of Newcastle fans stuck to their plan of walking out of the stadium in the 69th minute in protest of the club's management, with that particular moment of the game selected due to 1969 being the last time the side won a trophy.
Loic Remy sealed the points for Newcastle two minutes from time as Cardiff were punished for leaving gaps at the back as a result of pushing men forward in search of an equaliser. Steven Taylor scored Newcastle's third after converting from a yard out.
Fulham's 13-year stint in the Premier League has come to an end after they were beaten 4-1 by Stoke.
Peter Odemwingie put Stoke in front six minutes from the break after Stephen Ireland's shot had hit the crossbar.
Marko Arnautovic doubled Stoke's lead nine minutes into the second half with a stunning first-time finish from Odemwingie's pass as Fulham offered very little attacking threat. Oussama Assaidi struck the third for Stoke as they punished Fulham on the counter-attack in the 73rd minute.
Kieran Richardson scored a consolation for Fulham with a low volley on 80 minutes, but Stoke netted a fourth goal two minutes later through Jonathan Walters after the substitute broke the offside trap from Charlie Adam's pass.
Aston Villa defeated Hull City 3-1 at Villa Park with Andreas Weimann scoring twice before half-time to cap a fine performance from Paul Lambert's side.
Ashley Westwood finished from the edge of the box to put Villa in front after a minute, but Hull grabbed an equaliser on 28 minutes as Jordan Bowery put through his own net from Liam Rosenior's cross.
Rosenior was offside when he received the pass from Tom Huddlestone's free-kick, but Villa did not let their heads drop as Weimann put Villa back in front after Hull squandered several opportunities to clear their lines from a set-piece.
Weimann then scored his second in first-half stoppage time with a header after some good work from Bowery down the left flank.
Southampton defeated Swansea 1-0 at the Liberty Stadium after Rickie Lambert scored in the 93rd minute in bizarre circumstances.
The game appeared to be heading for a goalless draw after both sides failed to create clear-cut opportunities.
However, at the end Swansea's Ashley Williams lobbed his goalkeeper Michel Vorm, with Lambert deemed to have got the final touch as the ball bounced over the line.
In the lunchtime kickoff, Newcastle secured a 2-0 win against Tottenham to ease the pressure on manager Sam Allardyce.
A deflected Andy Carroll header off Harry Kane gave the Hammers the lead after Younes Kaboul was sent off for denying Stewart Downing a goalscoring chance.
Downing then wrapped up the win before half-time as his free-kick found its way through a weak Tottenham wall.