In the third of eight minutes of injury time, Van Persie shot past goalkeeper Jose Reina at the near post to end Liverpool's unbeaten home record and strengthen Arsenal's chances of qualifying for the Champions League.
Arsenal goalkeeper Wojciech Szczesny had saved a penalty and rebound effort from Dirk Kuyt before Liverpool took a 23rd-minute lead through an own-goal by Laurent Koscielny.
Van Persie leveled the scores eight minutes later, heading in Bacary Sagna's right-wing cross.
The Netherlands striker has scored 31 club goals this season.
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