In an end-to-end affair, the visitors edged a seven-goal thriller 4-3 to collect three points in Manchester.
The Gunners raced into a two-goal lead through strikes from Mariona Caldentey and Lotte Wubben-Moy, but we reacted well to fight back.
Mary Fowler headed home before the break to reduce the deficit, and Vivianne Miedema equalised shortly after the interval when coolly slotting into the back of the net.
The pendulum swung once again, though, and Arsenal restored their lead almost immediately through Frida Maanum who drilled low past Khiara Keating.
A sucker-punch, definitely, but we again responded and pushed forward to win a penalty, which was confidently tucked home by Fowler.
But with the game finely balanced, it was the visitors who snatched the three points when Stina Blackstenius fired home from close-range.
Watch the short highlights in the video player above.