Wayne Rooney had put the visitors 2-0 up with a first-half brace, before Yaya Toure replied for City on the hour. There were unruly scenes in the aftermath of van Persie's winner, with United centre-back Rio Ferdinand left bleeding after appearing to be struck in the face by an object thrown from the crowd.
City substitute Carlos Tevez was also fortunate to escape censure for a wild kick at Phil Jones in the dying stages, but the final whistle prompted full-bodied celebrations from Alex Ferguson's visiting players. "City always come back, we knew that, and it is a really special way to end this game in a dramatic way with the three points," van Persie told Sky Sports. "Wazza (Rooney) asked if I was going to shoot or cross from the free-kick, and I chose to shoot.
"It was a great atmosphere and everyone was supporting their team. But what you saw happen to Rio should not happen on the football pitch."
City had not been beaten at home in the league since December 2010 and were protecting the last unbeaten record in English league football, but they now find their hold on the title slipping after a week that also saw them eliminated from all European competition.