It was no surprise that van Persie was Arsenal's nemesis; the striker has now scored in the last five matches between the two teams and his 27th-minute header was responsible for deciding this encounter, inflicting a blow to the momentum Arsene Wenger's men have built up this term.
Neither side were at their best during the much-anticipated fixture and although Arsenal improved after the break, they lacked cutting edge, with Wayne Rooney going closest to scoring in the second half when he shot just wide.
One goal was enough for David Moyes' side, though, who are now unbeaten in nine matches, as Arsenal – who entered the match on the back of wins over Liverpool and Borussia Dortmund – failed to reinstate their five-point lead at the top of the Premier League.
Van Persie headlined Manchester United's four changes from their goalless draw against Real Sociedad on Wednesday, while Michael Carrick and Jonny Evans also came in after overcoming calf and back niggles.
Arsenal shaded a cagey opening in which United's Rooney was the only player to test a goalkeeper, albeit with a relatively tame effort from distance.
The Netherlands star rose above Oliver Giroud and produced a soaring header that crashed into the top-right corner, too well-placed for Kieran Gibbs – who was on the line – to do anything about.
Rooney nearly doubled United's lead on the hour mark after Arsenal's defence failed to clear a clever flick-on header from Shinji Kagawa, but, after feigning to shoot and creating space, the England star tugged his left-footed effort past the right post with Szczesny beaten.
