The Netherlands striker met Wayne Rooney's corner with a header into the top corner in the 27th minute to condemn Arsenal F.C. to its second loss of the campaign and reduce its lead to two points from Liverpool.
Since leaving north London for Manchester in August last year, Van Persie has scored in all three games against Arsenal F.C.
After a scratchy start to the season, United is coming good under new manager David Moyes and is now just five points behind Arsenal, which didn't create a clear-cut chance in a flat display at Old Trafford.
After picking up just one point in matches against chief rivals Chelsea, Liverpool and Manchester City, it was time for United to deliver and for Moyes to claim a first signature victory in his short, erratic time as Alex Ferguson's successor. A defeat would have left them 11 points behind Arsenal and their hopes of retaining the title seriously dented.
As it was, United produced a performance of authority and tenacity. And who else was going to settle the match than Van Persie
Still unable to forgive the striker for leaving for United last year for 24 million pounds (then $38 million), Arsenal's away contingent weren't shy in expressing their feelings toward the Dutchman early in the game with crude chants.
Van Persie responded the only way he could _ by scoring, just as he did in both meetings between the teams last season on his way to becoming the league's top scorer for the second season running.
By getting away from Olivier Giroud and looping a header into the top corner over Kieran Gibbs, Van Persie netted for a fourth straight match in the league and a seventh time this campaign.
That was one of the few sights of goal in a cagey first half in which Arsenal played well within itself, displaying an inferiority complex many thought had disappeared after its strong start to the season.
United, with Rooney to the fore, hounded the visitors into sloppy errors and kept playmaker Mesut Ozil on the periphery. Arsenal's only half-chance fell to Giroud, and he headed over from the edge of the area from Aaron Ramsey's cross.
The Londoners were given a lift at halftime, however, with United center back Nemanja Vidic not coming out for the second half after being clattered in the head by the hip of his goalkeeper, David de Gea, in the final seconds of the first half.
Phil Jones, who had been shielding the defense brilliantly in central midfield, dropped into the backline and Arsenal's silky midfielders finally had some space to perform.
United initially remained in the ascendancy, with Rooney dragging a left-foot shot just wide from the edge of the area on the hour mark.
But Arsenal slowly began to take command, probing around United's area. Two devilish crosses by Bacary Sagna were missed by Giroud then Nicklas Bendtner, Jones denied Giroud with a last-ditch tackle and the France striker slid a shot just wide of the post.
However, De Gea wasn't seriously tested throughout as Arsenal fell to its first loss since the opening day of the season against Aston Villa.
For the champions, it could be the victory that sparks their season.