The loss ended United's 12-match unbeaten streak under Solskjaer, which is the longest for any interim manager in EPL.
Arsenal also maintained their record of not losing consecutive home games to a side in a single season, since 1993-94.
A dominating start by United, Arsenal have opening laugh
United were off to a dominating start as Romelu Lukaku hit the crossbar in the ninth minute of the game.
However, just three minutes later, it was Granit Xhaka, who gave Arsenal the opening advantage through a powerful strike, right from outside the box, through United's defense, which confused goal-keeper David de Gea.
United's Fred hit the post again in the 19th minute.
United's desperateness get better of them, Arsenal double the advantage
It was expected that United would come out all guns blazing in the second half and the same did happen.
It was Fred again in the 51st minute, but his shot was saved by Leno.
However, Arsenal failed to give up and created multiple chances. Eventually a penalty allowed the hosts to double their lead as Pierre-Emerick Aubameyang converted from the spot.
What does this mean for both the sides?
The win is a huge boost for Arsenal as they recover from their embarrassing UEFA Europa League defeat to Rennes, last week, while they rise to the fourth spot in the table, a point behind Tottenham Hotspur.
As for United, they were not clinical, but have nothing to be disheartened about, especially following their turnaround under Solskjaer, as they go down to fifth.
What's next for both?
While United have a week's time from now to prepare themselves as they take on Wolverhampton Wanderers in the quarter-finals of the FA Cup, next Sunday, at the Molineux Stadium.
As for Arsenal, they prepare for the home leg of their Europa League clash against Rennes on Thursday. Notably, they are already 1-3 down in the away leg and need a miracle.