Everton twice came from two goals behind in an extraordinary 4-4 draw away to United at Old Trafford.
City, who knew United's result before they kicked off, then won 2-0 against Wolves to relegate the Black Country club and revive their bid for a first English title in 44 years.
That win saw them move to within three points of United ahead of the Manchester derby at City's Eastlands ground a week on Monday, where victory for the hosts will see them replace the champions at the top on goal difference with two matches left.
Argentina forward Sergio Aguero's 27th minute opener put City ahead at Molineux before Samir Nasri's goal 16 minutes from time made the game safe for the visitors as Wolves, who had to win to stay up, were relegated with three games left to play.
Nevertheless City manager Roberto Mancini insisted United still had the upper hand, telling Sky Sports: "They have three more points and after the derby they have two easy games (at home to Swansea and away to Sunderland while City travel to Newcastle and finish at home to QPR)."
Wolves had to win to avoid the drop but that rarely looked like happening and Terry Connor, promoted from coach to manager after Mick McCarthy was sacked, said: "It's a very difficult day, a raw day for me the staff the players everyone connected with the club and it will be a tough few days to come."
Everton were 4-2 down with seven minutes of normal time left and Manchester United manager Sir Alex Ferguson said afterwards: "We've thrown it (this match), away, absolutely given it away."
Looking ahead to the derby, Ferguson said: "We've given them (City) the initiative. It makes the game at the Etihad Stadium more important -- it's the decider really."
Everton, who last won at Old Trafford 20 years ago, took a 33rd-minute lead when Nikica Jelavic headed in Tony Hibbert's cross as the visitors looked to bounce back from their FA Cup semi-final defeat by cross-town rivals Liverpool.
But United were level before the break when Wayne Rooney, against his former club, powered in a header from Nani's cross.
Danny Welbeck's superb curling shot past former United keeper Tim Howard gave Ferguson's men a 2-1 lead before Nani's clever finish on the hour made it 3-1.
Everton, however, would not lie down and Marouane Fellaini's first time shot from Hibbert's cross cut United's lead to 3-2.
But when Welbeck teed up Rooney for the England striker's second goal in the 69th minute, it appeared United had wrapped up all three points.
Indeed United might have gone 5-2 in front only for Patrice Evra's close-range header to come back off a post.
But Everton fought back with Jelavic scoring his second before, five minutes from normal time, South Africa's Steven Pienaar swept in Fellaini's cross to make it 4-4.
United almost won the match in the fifth and final minute of stoppage time but Howard saved from Rio Ferdinand.
Everton manager David Moyes was delighted by the way his side responded to their FA Cup semi-final defeat by Liverpool.
"It was absolutely brilliant, the effort they put in," he said.
Elsewhere, Liverpool's league campaign took a fresh turn for the worse as former manager Roy Hodgson, sacked last season by the Reds, oversaw West Brom's first win at Anfield in 45 years with Peter Odemwingie scoring the lone goal in a 1-0 victory.
"It's not the first time we've stood here and said exactly the same things. It has been the same theme, hitting the crossbar, people clearing it off the line, us missing chances or hitting our own players," said Liverpool manager Kenny Dalglish.
Hodgson added: "I can't deny that we rode our luck and Liverpool played very well and put us under pressure but it was a fantastic rearguard action."