United had no answer to Arsenal's opening burst as Alexis Sanchez and Mesut Ozil scored twice in 74 seconds.
Sanchez added a third from 18 yards as the Gunners beat United for just the second time in 14 league meetings.
United improved after the break but Arsenal substitute Alex Oxlade-Chamberlain hit the crossbar late on.
Defeat leaves Louis van Gaal's side in third place, behind Arsenal on goal difference.
With their first real attack Sanchez back-heeled in at the near post after good work from Aaron Ramsey and Ozil, and the Germany playmaker then added the second a minute later after Walcott ran at a struggling defence.
Sanchez shrugged Matteo Darmian aside to add his second with a brilliant 18-yard strike which brought up an unwanted record for the visitors, as they conceded three goals in the opening 20 minutes of a Premier League game for the first time.
And it should have been four just after the half-hour mark as Ramsey volleyed wide from close range when completely unmarked.
With the game won, Arsenal failed to repeat their attacking display in the second half until substitute Oxlade-Chamberlain chipped David de Gea and hit the crossbar in injury time.
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