Victory in their neighbours' backyard, at an Etihad Stadium where City had not lost in the league for almost two years, sent Sir Alex Ferguson's side six points clear of their opponents at the top of the table in what already looks like a two-horse race.
Two first-half goals from Wayne Rooney had put United ahead before City pulled level thanks to Yaya Toure and Pablo Zabaleta, only for Van Persie to shatter their comeback.
It was payback time for United, who were denied a 20th English title in the final seconds of last season when City grabbed the championship on goal difference after two stoppage-time goals.
On top of that, their winner came from a player City had courted before his close-season move from Arsenal to the red side of Manchester and it completed a miserable week for Roberto Mancini's side who crashed out of Europe on Tuesday.
Van Persie's 11th league goal of the season could end up being one of the most important if last term is anything to go by when City won both Manchester derbies, including a 6-1 demolition of United at Old Trafford, on their way to the title.
"Today was special because they hadn't lost at home for two years and both of us are contending at the top of the league," Ferguson, whose side have 39 points from 16 games to City's 33, told Sky Sports.
"It was a fantastic game and you couldn't take your eyes off it. We should have killed the game off but it's a funny game football, instead of being 3-0 it was 2-1 and it got the fans going."
United's celebrations were marred, though, when defender Rio Ferdinand was left bloodied above his left eye after being struck by an object thrown from the crowd in an incident that police said they were investigating.
The "Champ1-0ns" banner taunting the United fans summed up the significance of this match, referring to the 1-0 victory by City over their neighbours at the Etihad Stadium late last season which tilted the title race in their favour.
While City manager Mancini was confident they could still catch their rivals, and they overturned an eight-point gap with six games to play last season, he was frustrated to have conceded so late.
"It is a bad feeling in this moment. When you lose a derby in the last second, it is very difficult," the Italian, whose side had not lost at home in the league since December, 2010, told a news conference.
"We have the spirit to recover these six points. We need to do four or five wins in a row."
It was City who made the better start on a sunny afternoon in Manchester, with Mario Balotelli sending a good chance flying well over the bar.
But United caught City and, in particular, keeper Joe Hart by surprise on their first foray forward.
Winger Ashley Young set up Rooney, who struck a tame shot that Hart appeared to think was going wide but that trickled, almost in slow motion, into the bottom corner.
City's problems were compounded when captain and centre back Vincent Kompany was forced off the field with a groi
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