A Granit Xhaka strike and a second-half penalty from Pierre-Emerick Aubameyang, who missed from the spot in the 1-1 draw with Tottenham last week, gave the Gunners three valuable points that lift them into fourth.
Arsenal started positively but should have been behind nine minutes in, when Romelu Lukaku steered Luke Shaw's low cross against the crossbar from six yards out.
The Gunners punished that miss three minutes later, when Xhaka's swerving strike from 25 yards out completely bamboozled David de Gea and nestled into the left-hand corner.
6 - David De Gea has conceded six Premier League goals from outside the box this season - double the amount he did in the competition last term. Turbine. #ARSMUN— OptaJoe (@OptaJoe) March 10, 2019
Fred struck the base of the post as United sought a quick response, and both Marcus Rashford and Lukaku should have done better after finding space inside the penalty area.
Lukaku was denied by a good Bernd Leno save when Rashford picked him out with a clever pass, and the German was out again to smother the ball at the feet of the England striker as United's pressure grew.
Arsenal made the most of those missed opportunities 21 minutes from time, when Aubameyang sent De Gea the wrong way from the penalty spot after Alexandre Lacazette went to ground under minimal contact from Fred.
What does it mean? Advantage Arsenal in the top-four chase
The Gunners have now moved two points above United into fourth place, just one behind Tottenham in third, with only eight matches left to play.
For United, their winning run under Solskjaer ends in a game where, for once, he seemed to hinder his side with his selection.
Leno outshines De Gea
Leno made three good saves and a couple of timely interceptions just when United's pressure was building. For once, De Gea was outshone at the Emirates.
Solskjaer, at last, gets it wrong
Starting with Pogba wide left made him ineffective early on, and by the time Solskjaer switched up the system, United were chasing the game.
Key Opta Facts
- Arsenal have won 12 points from their 10 games against fellow 'big six' sides in the Premier League this season, double the amount they won in such games last term.
- United suffered their first Premier League defeat under Solskjaer (W10 D2 L1).
- Arsenal have won their last nine Premier League home games, their joint-longest winning run at Emirates Stadium within a single season (also nine in 2014-15).
- United failed to score for the first time in 22 away games in all competitions this season, last failing to find the net on the road in May 2018 at West Ham.
- Six of Xhaka's seven Premier League goals for Arsenal have come from outside the box, including both of his strikes against United.