The clash was one of three fixtures moved to Premier League grounds this weekend and more than 40,000 fans witnessed one of United’s biggest wins and the end of Arsenal’s 14-match winning run in the WSL.
Ella Toone deservedly put United ahead late in a first half as the visitors dominated, but Arsenal were level seconds after half-time through Frida Maanum.
Laura Wienroither looked like she might have won it for Arsenal in the 73rd minute, but Millie Turner equalised in the 85th minute and Alessia Russo scored the winner in injury time.
The victory moves United level on points with the Gunners and Chelsea at the top of the table.
Vivianne Miedema returned to the Arsenal squad after being given time off, but Jonas Eidevall stuck with the team that beat Leicester last time out, while United were looking to bounce back from their first defeat of the season against Chelsea.
The visitors had much the better of the first half and would have felt they might have had more to show for it than Toone’s 39th-minute effort.
The England forward played in Leah Galton for the first opening in the seventh minute, but Manuela Zinsberger was equal to the shot.
Maya Le Tissier then sent a floating header onto the roof of the net, and Zinsberger’s discomfort under high balls cost her team when she flapped at a Hayley Ladd cross and Toone tucked the ball away into an empty net.
United then appealed for a penalty when Nikita Parris clashed with Caitlin Foord, but the referee was unmoved.
Arsenal had created almost nothing, but they were level within seconds of the resumption.
United backed off as Maanum drove towards the box and paid the price when her speculative shot took a huge deflection off Le Tissier and nestled in the far corner.
Miedema made her entrance in the 58th minute with Arsenal pressing for a second, and it arrived 17 minutes from time.
After patient build-up down the left, Katie McCabe swung in a perfect cross for Wienroither to rifle into the net, giving Mary Earps no chance.
Arsenal looked more likely to score a third than United find an equaliser, but a free-kick gave the visitors an opportunity and they took it brilliantly, Katie Zelem’s fine delivery met by a powerful header from Turner.
Suddenly the momentum was with United and, after Zinsberger had produced fine saves to deny Lucia Garcia and Martha Thomas, Russo headed in Zelem’s corner.
Additional reporting from PA