Yet despite the disastrous start, plus the loss of the injured Mustafi that forced a change in formation and a switch to a flat-back four, the hosts peppered United's goal for the remainder of the half.
It was United manager Jose Mourinho's first away victory in 11 games against the "Big Six" and the first loss home loss for the Gunners after winning their last 12.
United's fourth successive league win puts pressure on City to maintain their blistering form against West Ham on Sunday.
Explaining that he hoped that they would begin to drop points, Pogba then added that - in the nicest possible way - he hoped City would pick up a few injuries along the way, too.
That may be the case with City in the ascendency, but this was still a classic encounter.
Laurent Koscielny's careless cross-field pass inadvertently set up Valencia's opener before Shkodran Mustafi's carelessness in possession led to Lingard scoring, the England global not even having to break stride to convert Anthony Martial's exquisite reverse pass in behind.
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Lingard scores the second for United.
Arsenal weren't ready to surrender and they should have been back in it when Lacazette took aim from close-range, only to see his shot blocked onto the bar by De Gea before Granit Xhaka smashed the rebound just wide.
Lingard nearly produced the ideal response for United, but Cech saved and the ball bounced to safety off the bar. The United resistance prompted the Frenchman to state De Gea was "man of the match by a clear mile".
United's first two goals came early on from sloppy play in possession by Arsenal.
The incisive raid reached a fitting crescendo when Lukaku sent Pogba into the penalty area and his low cross found Lingard unmarked to tap in at the far post.
That said, Wenger was amazed they did not make more of the chances they created, especially once Paul Pogba was given a straight red card with 15 minutes remaining.
But with De Gea in defiant mood, United had done enough for a memorable success.