England striker Alessia Russo scored with United’s first shot on target on the stroke of half-time after Nikita Parris had got free down the right wing and pulled the ball back.
It looked like she was going to be carried off on a stretcher, although that eventually was not needed, but Williamson looked in great discomfort as she limped off the field.
United are top of the WSL on 44 points from 18 matches, with Chelsea on 40 points from 16 games and Arsenal third on 38 points from 17 matches.