The visitors hit the front at Bramall Lane after just over 60 seconds of the game, as the recalled Chris Sutton linked up with Stilian Petrov and the latter beat Paddy Kenny after his first effort had struck Leigh Bromby.
That blow seemed to rock the Blades back on their heels, with Sutton heading against the crossbar from Petrov's free-kick as Villa continued to dominate.
Kenny also kept his side in the game with a superb double save from Sutton on the half-hour, after Petrov had again proved to be a menace to the home defence.
However, after a half-time pep talk from boss Neil Warnock, United came out fighting in the second period and drew level within five minutes of the restart.
Stephen Quinn netted his first senior goal as he fired home after Liam Ridgewell had failed to deal with a Rob Kozluk long throw into the area.
Rob Hulse tested Stuart Taylor as the Blades began to dominate, before Danny Webber made it 2-1 to the home side as he hooked home after Chris Morgan had headed back across goal following a short corner routine.
However, the lead lasted less than a minute as Steven Davis played the ball into the area and Sutton drew the defence to allow Milan Baros time and space to smack his shot past the exposed Kenny.
That proved to be the final goal of the game, but both sides went in search of a winner in the latter stages.
Hulse and sub Christian Nade went close for the home side, before Taylor was forced into an excellent save from Quinn.
Gabriel Agbonlahor wasted an opening for Villa at the other end, before Petrov's free-kick went narrowly wide as the game ended all-square.