Christian Benteke put Villa ahead after 18 minutes at Villa Park, curling home superbly from just inside the area after escaping the attention of Jonny Evans.
Radamel Falcao pulled United level after the break, getting in behind Ciaran Clark to head past Brad Guzan from Ashley Young’s superb left wing cross.
Gabriel Agbonlahor was sent off for Villa in the 65th minute, going in hard on his former team-mate Young in a 50-50 challenge and catching the United man on the ankle.
But Villa held on for a point, and even had a few chances of their own late on through Leandro Bacuna and Benteke.
For all their possession in the opening 45 minutes, United could only create half chances as Villa’s defence worked tirelessly to snuff them out.
Looking to keep up with Chelsea and Manchester City at the top of the Premier League, the away side went with Falcao up front alongside Robin van Persie.
Early on, former Villa midfielder Young’s low ball into the box evaded the home defence as well as Van Persie, while the Dutchman’s volley from a fine Wayne Rooney diagonal pass was saved well by Guzan in the Villa net.
Villa took the lead after Fabian Delph’s deep free-kick from the left fell to Benteke deep inside the box. The Belgian shook off United defender Evans, twisting one way and then the other, before his left-footed effort through a packed penalty area left David de Gea helpless.
But United kept pressing and Falcao, put through by Van Persie inside the penalty area, couldn’t escape the pressure of Villa defender Jores Okore, seeing his tame shot fall into the arms of Guzan.
In a half of few chances, Delph saw his effort blocked well by Evans inside the area while Young, continuously given plenty of time on the ball by Villa right-back Matt Lowton, saw his delivery come to nothing on numerous occasions in the first half.
The game came to life again in the second-half; first Benteke offloaded to Delph in space, whose effort was blocked by Evans, before Benteke’s rising header from the resulting corner was tipped over by De Gea.
At the other end Guzan did superbly well to prevent Van Persie equalising after the Dutchman was put through one-on-one with the American stopper, but United did draw level on 53 minutes.
Young got more joy down the left, getting the better of Lowton to provide a perfect cross for Falcao, who headed back across the goal and past Guzan.
It was the Falcao’s second goal for United since joining on loan from Monaco in the summer, but no chances came the Colombian’s way thereafter.
Agonblahor was then dismissed in controversial fashion, swinging his leg into a challenge with Young near the centre circle, with referee Lee Mason deeming it to be dangerous play. It was Villa’s second red card in as many games.
United forced two good saves out of Guzan after having the extra man, but it was the hosts who continued to press.
Substitute Bacuna went close with a 25-yard effort which sailed just over De Gea’s goal and in injury time Bacuna’s low cross into the box evaded Charles N’Zogbia after United had committed men forward.
And Villa held on for a credible draw when defeat looked more likely, while United dropped seven points behind second-place Manchester City, who beat Crystal Palace earlier on Saturday.
Soccer Saturday verdict – Matt Le Tissier
“Villa will consider themselves unfortunate in terms of going down to 10 men, but not in terms of the game itself. United dominated the possession and had the majority of the chances. They will feel disappointed they didn’t take all three points, but you have to give credit to Aston Villa, especially when they went down to 10 men. There was 25 minutes to go at that point and they dug in really well, defended for their lives and showed a little bit of attacking intent on the break.”