Villa took the lead twice in the first half, but goals from Leah Galton and Nikita Parris pulled things level each time.
Just when it looked like the points were going to be shared, an injury-time free kick found Millie Turner, whose thumping header hit the back of the net to secure a 3-2 victory.
“The great Manchester United men’s teams never game up, it’s called Fergie time for a reason,” Skinner told reporters last night. “The reality is that there is a mentality behind that concept.
“We have that mentality to keep fighting, keep progressing, keep trying to get free kicks, keep trying to score.