The result left Arsenal on 25 points from 11 matches, two clear of Liverpool, with United moving ominously up to fifth on 20 ahead of local rivals Manchester City, who were stunned 1-0 at struggling Sunderland and drop to eighth on 19 points.
The day's big match was a litmus test for both sides, with the North Londoners arriving as the form team eager to end years of hurt at United and charge 11 points clear of their old rivals who are under new management.
Alex Ferguson may have been watching from the stands rather than shouting from the bench but David Moyes' side ensured the outcome remained depressingly familiar for the Gunners, who have now won only one of their last 10 league encounters with United.
It was Arsenal's first away defeat since March after a run of 15 games unbeaten in all competitions and thrust United right back into the title race after a faltering start to the campaign.
Van Persie bagged his seventh league goal of the season when the Dutchman rose to meet a Wayne Rooney corner kick and head home at the far post in the 27th minute.
Arsenal failed to live up to expectations, creating few chances on a strangely muted evening for their record signing Mesut Ozil, and could even have found themselves 2-0 behind after an hour when Rooney shot just wide.
(Reporting by Alan Baldwin, editing by Ken Ferris)
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