Having been level at the interval, the visitors broke the deadlock after half-time through a Vivianne Miedema strike, before Katie McCabe added a second from the penalty spot.
The result ends a run of six games unbeaten in all competitions for the Reds, against an Arsenal side who have dropped just two points in the league this season.
FIRST HALF
From the off United were controlling possession, dictating play with crisp passing and pressing the visitors to win the ball high up the pitch. In the opening minutes Leah Galton worked a good opportunity down the left to cross the ball in, but her delivery was over the head of Kirsty Hanson.