Wayne Rooney clinched an unconvincing 1-0 victory over relegation-threatened Reading with a shot that deflected into the net off Alex Pearce in the 21st minute.
"We knew the three points was the most important thing today — especially after City dropped three points," Rooney said.
With nine games to go, only a monumental collapse by United would now allow City to retain the trophy.
Even then, City would have to show more desire than at Everton on Saturday after the defending champions lost 2-0 despite having a man advantage for the final half hour.
United, though, appears to be unstoppable, especially with the defence not being breached for five successive league games.
"The players are conscious of the importance of the games now ... you don't get points and medals for being complacent," United manager Alex Ferguson said. "And we won't be."
In the relegation fight, Reading is level on points with bottom-place Queens Park Rangers, which lost 3-2 at Aston Villa. Villa is only a place above the drop zone but six points clear of Wigan, which hosts Newcastle on Sunday.
Southampton is a point further ahead of Villa after beating Liverpool 3-1. Everton is three points ahead of Liverpool but was prevented from moving up to fifth by Arsenal beating Swansea 2-0.
Both Arsenal and Everton provided the perfect response to cup setbacks.
Arsenal's title hopes ended for an eighth straight season on Wednesday by exiting the Champions League at Bayern Munich, while David Moyes' hopes of a first trophy of his 11-year Everton reign were thwarted by an FA Cup quarterfinal collapse to Wigan last weekend.
Everton went ahead in the 32nd minute though Leon Osman's bending strike, and City couldn't take advantage of the hosts being reduced to 10 men on the hour when Steven Pienaar was sent off.
Carlos Tevez, James Milner and Pablo Zabaleta were denied by a succession of saves from Everton goalkeeper Jan Mucha.
City was aggrieved not to be awarded a penalty in the 86th when Tevez's shot was blocked by Marouane Fellaini's hand inside the area, only for the referee to award a free kick just outside instead.
Nikica Jelavic secured the win in stoppage time by completing a speedy counterattack by curling in Everton's second goal.
"We have an obligation to win football matches between now and the end of the season, regardless of whether there is a points advantage or it is mathematically impossible (to win the title), which it isn't at this moment," City assistant manager David Platt said.
How Arsenal would relish being in City's position now, seemingly assured of a top four finish to qualify for the Champions League.
The Gunners are only two points behind fourth place, but Chelsea is yet to play West Ham on Sunday.
Nacho Monreal set Arsenal on its way to victory in south Wales with his first goal since arriving in the January transfer window. The Spain defender lashed the ball beyond goalkeeper Michel Vorm with the help of a deflection off Ashley Williams in the 74th.
Gervinho wrapped up the win in stoppage time by slotting low into the net.
Swansea remains ninth in the standings, with a third successive season of Premier League football secured.
Villa, which has been in the topflight since 1988, boosted its hopes of avoiding the drop with eight games to go by edging out QPR.
Although Jermaine Jenas put QPR in front, through Gabriel Agbonlahor equalized on the stroke of halftime and Villa took the lead after the break through Andreas Weimann.
Andros Townsend pulled Harry Redknapp's team level again in the 73rd but Christian Benteke struck the winner in the 81st.
Southampton remains clear of danger after ending Liverpool's run of three successive wins.
Morgan Schneiderlin and Ricky Lambert netted for the south-coast team and, after Coutinho pulled one back before half time, Jay Rodriguez made the win certain in the 80th.
West Bromwich Albion went a point behind Liverpool, with the eight-place team drawing 0-0 at Stoke.Suggest a correction