Second-placed City's second successive league win at Old Trafford, following last term's 6-1 demolition job, allowed them to narrow the gap on United to 12 points with seven games left although manager Roberto Mancini said the title race was over.
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"The championship is finished," the Italian told a news conference. "Our supporters deserve this victory, after we were 15 points behind it was important for them.
"It is important for us because we can clinch second position."
A blistering opening 10 minutes gave way to a scrappy first half before the visitors broke the deadlock in the 51st minute with James Milner's deflected goal.
The lead lasted eight minutes before an unfortunate own goal from City captain Vincent Kompany following a superb free-kick by Robin van Persie but substitute Aguero came on to snatch the points with a special goal in the 78th minute.
United lead the way with 77 points from 31 games with City on 65. Third-placed Chelsea are on 58 points, level with Tottenham Hotspur who have played a game more than their London rivals.
While City have effectively already handed over their crown, United manager Sir Alex Ferguson is avoiding taking possession until the mathematics are complete.
"We won't be complacent. If you look at the history of this club over the years we always make it difficult for ourselves," he told the BBC.
"The supporters are hanging on the edge of their seats every year. It is a 12-point lead, we go to Stoke at the weekend and we will have a go."
On a chilly evening at Old Trafford, visiting fans taunted their hosts by singing 'We are the champions - champions of England' and reminded them of last season's hammering that proved key when they won the title on goal difference.
The frenetic start to the game highlighted there was more than just three points at stake as United sought to eradicate memories of that drubbing and City reproduced fleeting glimpses of last term's attacking spark.
BARREN SPELL
The visitors had the better chances as Samir Nasri, Milner and David Silva wasted decent opportunities while United forward Van Persie, enduring a barren spell of 10 games without a goal, experienced yet more frustration.
The Dutchman's early shot across goal went just wide of the far post and he later fired wildly into the crowd from distance.
United's stand-in centre-back Phil Jones was quick off the mark to intercept after good work from Silva who tried to set up former Old Trafford favourite Carlos Tevez.
City were finally rewarded for their domination of possession when Ryan Giggs messed up an attempted backheel to allow Gareth Barry to run free down the left and lay the ball to Nasri who set up Milner for a shot that went in off Jones.
The goal brought to an end a six-match r
