Scotland international Jane Ross opened the scoring - her first goal for City - after the break before Toni Duggan's penalty sealed the victory as City moved top of the early table after winning their opening two games.
The Gunners had Jemma Rose sent off after just 13 minutes for a foul on Ross.
Fara Williams hit the bar with an early free kick for Arsenal before Rose was dismissed for taking down a breaking Ross and Duggan almost grabbed the opener just before the break when her low effort struck the post
After the restart Sari van Veenendaal denied Nikita Parris as City tried to force the issue a nd they got the opener when Rose met Duggan's cross to head in after 65 minutes
And they doubled their lead with 12 minutes left when Duggan scored from the spot after Dominique Janssen tripped Parris in the area
Elsewhere, Liverpool Ladies' trip to Chelsea was postponed due to a waterlogged pitch