It was a mixture of old and young talent on the pitch that secured United the victory with 21-year-old Ella Toone also scoring.
However, United have a game in hand over the London side and would need them to drop points to make a title challenge -- a tall order with Chelsea on a record-breaking unbeaten run of 33 matches in the WSL.
Press, who decided not to travel to the USWNT's January camp, had several good chances throughout the first half to double United's lead and eventually converted three minutes before half-time.
Everton failed to clear the ball and Press ran onto it. Despite falling as she got her shot away, Press managed to direct it into the bottom corner of Maciver's goal.
Willie Kirk's side improved in the second half but were unable to pull a consolation goal back.
Press was substituted on 80 minutes for Lauren James.