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.
"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.
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.
