Vincent Kompany's header in first half added time earned Roberto Mancini's team the points and catapulted it above United to top spot on goal difference.
City now needs only to match the results of its Manchester rival in the final two games of the league campaign in order to pip Sir Alex Ferguson's men to the top flight crown.
City had scored 12 goals in three matches prior to this fixture and as a result Roberto Mancini opted to stick with the side that had relegated Wolves eight days earlier. That meant that Carlos Tevez faced his former club alongside Sergio Aguero in attack, with David Silva and Samir Nasri in support.
Antonio Valencia was surprisingly omitted from the United starting XI, with Park Ji-Sung and Ryan Giggs joining the midfield and Wayne Rooney deployed as a lone striker. Jonny Evans, who had been struggling with a foot injury, was replaced by Chris Smalling at center back while Phil Jones was preferred to Rafael at right back.
Silencing the raucous City supporters will have been close to the top of the United to-do list and the defending champion was able to settle quickly in the opening minutes.
Nani exchanged passes with Giggs from a corner to deliver a cross that Joe Hart could only punch to Michael Carrick, whose volley was blocked by Vincent Kompany. The Belgian's arm was raised to his chest but referee Andre Marriner was unmoved.
The home side, indeed, did not muster its first threatening attack until the 15 minute mark when Tevez's low cross was cut out by Jones after Nasri had snaked through the United midfield.
Kompany was booked for a foul on Rooney in the first of a series of decisions given by Marriner to the displeasure of the City supporters but Mancini's team remained focus on the matter at hand and finished the half the stronger of the two sides.
Aguero hacked a volley wide from close range and Pablo Zabaleta failed to get good contact on a left-footed effort from a similar distance. The United resistance was stern and it seemed City had fallen into a lull, despite its monopoly on possession, as the fourth official indicated the amount of first half added time to be played.
However, Joleon Lescott's cunning positioning prevented Smalling from tracking Kompany as Silva whipped in a corner from the right and the City captain rose unchallenged to thump a header past David De Gea.
United struggled to find counterattacking opportunities due to the nature of City's narrow and congested midfield unit, leading Ferguson to introduce Danny Welbeck just before the hour mark.
Mancini, despite the visitors' lack of attacking opportunities, was not counting his chickens. Nigel de Jong replaced Tevez and dropped to a position in between Yaya Toure and Gareth Barry.
In desperation, United began to look increasingly stretched. Toure rocketed a low shot just wide of De Gea's left post having been given more license to push on after De Jong's introduction.
The Dutchman himself was more concerned with affairs in his own half and earned a yellow card for a foul on Welbeck that seemed to infuriate Ferguson. The 70-year-old exchanged several choice words with his counterpart, Mancini, on the touchline in a reaction that spoke volumes as to the immense importance of the match being played out in front of them.
Toure narrowly missed from 20 yards once more before Ashley Young entered the fray as a last roll of the dice for United.
Yet it was City that went closest to adding to the scoreline. Gael Clichy was denied by De Gea from the edge of the box before Nasri took too long to pull the trigger from point blank range, but the missed chances would not matter as City held on for the win.
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