City had wiped out United's 2-0 first-half lead and looked to be heading for a draw when Robin van Persie struck with a deflected free-kick in injury time to clinch a crucial win for United and send them six points clear of their neighbours at the top of the table.
The late goal meant this was City's first home defeat in two years in the league and a big blow to their title hopes after their spirited second-half fightback. Roberto Mancini's men drifted out to 2/1 from 7/4 to retain their crown.
Sky Bet football trader Paul Lowery said: "United have put a major dent in City's chances and six points will be tough to overhaul heading towards the halfway stage of the season.
"8/15 is the shortest United have been all season and the derby win will gave them great momentum heading into a busy festive calendar."