As the second half began, Tomas Rosicky's curling effort with the outside of his boot went close to restoring Arsenal's lead but United responded, with Van Persie's low cross almost finding Wayne Rooney inside the six-yard box.
Shortly after the hour mark, and with United becoming the better team, Arsenal boss Arsene Wenger introduced star man Jack Wilshere in place of Rosicky among his second-half substitutes.
But other than a curler from Santi Cazorla, which had to be saved by David De Gea, United remained the greater threat on the counter-attack and substitute Ryan Giggs saw a late effort deflected just wide as the game ended in a draw.
With the title already wrapped up, champions Manchester United were happy to settle for a draw, but the result was a setback for Arsenal, who dropped down to fourth place following Chelsea's 2-0 win over Swansea.
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