They appeared set for a massive setback in their quest for a maiden WSL title when Rachel Daly scored twice in the first half for Villa, either side of a Leah Galton strike.
However, Nikita Parris pulled United level again on the hour mark, before Turner powered in a Katie Zelem free kick in the fourth minute of added time to seal three points in one of the most exciting games of the season.
Villa hit the bar twice, while United were denied a goal shortly before half-time due to a questionable foul on home goalkeeper Hannah Hampton.
United are now six points ahead of Manchester City, who play on Sunday, while they are seven clear of reigning champions Chelsea, who do not play this weekend due to Champions League commitments and now have three games in hand on the leaders.