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.
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.
The Reds had defending to do however when Katie McCabe slid a pass to Beth Mead in the area. Mead’s shot crashed off the crossbar and back into play, but a combination of Maria Thorisdottir and Hannah Blundell did well to clear the ball and stop Vivianne Miedema pouncing on the rebound.
That opportunity gave the Gunners some vigour after a slow start, but despite winning a couple of set-plays the best chance of that spell was a Frida Maanum effort which she lifted over the bar as she cut inside.
Breaking away, Blundell covered plenty of ground as she carried the ball out of defence and played a through ball towards Ella Toone, who would have been in behind if not for the work of Kim Little who tracked back well to outmuscle her opponent.
Back up the other end, Mary Earps was called into action to deny Steph Catley as she rose to meet a corner with her head in the box, but Earps was easily equal to it and caught comfortably.
Earps then denied Arsenal with another important save at the back post after an attempted cross had broken to Little and while Jonas Eidevall’s side did end the half the stronger, United’s defence was able to cope with the challenge thrown at them.
Reds edged out by Arsenal gallery
United were beaten at Leigh Sports Village.
In just the third minute of the second 45, Miedema stuck to put the visitors in front. Running across the edge of the box she fired a low effort past the defence and out of reach of Earps for 1-0.
There was a concerning moment for Hanson as she was left on the ground following a foul by McCabe, with the Arsenal player shown a yellow card after clattering into the knee of Hanson. Fortunately she was able to carry on after treatment.
Referee Emily Heaslip then ruled McCabe had been fouled by Aoife Mannion as the defender slid in to block a potential shot in the box, awarding a penalty and the Gunners an opportunity to double their advantage.
McCabe herself then stepped up to take the spot-kick, with usual penalty taker Kim Little off the field after being substituted at half-time. Earps dived the correct way, but couldn’t get a hand to it as McCabe fired home left-footed.
Working hard to get back into the game, Lucy Staniforth and Katie Zelem came so close to completing what would have been a magical goal. Staniforth picked out the skipper with an inch-perfect ball over the top which Zelem played first time. Only an exceptional save from keeper Manuela Zinsberger kept it out.
United kept pushing but despite their efforts couldn’t find a reply. Substitute Carrie Jones, who signed her first professional contract for the Reds this week, created probably the best opportunity of the closing stages, feeding the ball to Galton in the six-yard-box, but the flag went up for offside.
United: Earps; Blundell, Mannion, Thorisdottir, O. Batlle; Staniforth, Zelem (c) (Boe Risa 87); Hanson (Jones 78), Toone, Galton; Russo.
Subs not used: Baggaley, Ladd, F. Fuso, Smith, Turner.
Arsenal: Zinsberger; Catley, Wubben-Moy, Beattie, Maritz (Patten 90+5); Little (Nobbs 46), Walti, Maanum; McCabe (Parris 78), Miedema (Foord 86), Mead.
Subs not used: Williams, Stenson, Goldie, Houssein.
Goals: Miedema 48, McCabe 57.