The result leaves Arsenal third on 23 points after 12 matches, one point ahead of United in fourth. Manchester City lead the table with 30 points, while defending champions Chelsea are second on 24. City and Chelsea have a game in hand.
United right back Jayde Riviere was sent off in the 65th minute after picking up a second yellow card for a late challenge on forward Caitlin Foord, but Arsenal failed to make their numerical advantage count.
Both sides created chances. United came closest early on when Fridolina Rolfo's header was tipped on to the bar by Arsenal goalkeeper Anneke Borbe. At the other end, United's Phallon Tullis-Joyce denied Olivia Smith from close range after a defensive mix-up.
The match marked the return of Arsenal captain Leah Williamson, who made her first league start of the season after recovering from a knee injury sustained during Euro 2025, which England won.
Her comeback is a boost for manager Renee Slegers, who signed a new three-year contract earlier on Friday to remain at the club until 2029 after guiding Arsenal to their second Women's Champions League title last year.