The visitors took the Reds by surprise in the first half with their high press but United defended well and headed into the break level.
Marc Skinner's side came out with more aggression in the second half and the substitutes helped raise the levels, but it wasn't enough to break Villa down in the end.
After six league matches, United Women remain unbeaten.
FIRST HALF
Following a minute's silence for Remembrance Sunday - beautifully observed by both sets of fans - United got things under way.
Phallon Tullis-Joyce was almost tackled by Gabi Nunes as the Reds' keeper tried to play out from the back, but the American was able to clear under pressure.