James Collins and Gabriel Agbonlahor each struck the United woodwork before Villa went ahead when Ashley Young scored from the penalty spot.
Marc Albrighton slotted in from close range as he added to Villa's lead.
But Federico Macheda gave United hope with a powerful shot and Nemanja Vidic stooped to head in a Nani cross to equalise for the visitors late on.
United's comeback provided a thrilling finale to the match but manager Sir Alex Ferguson must have been left wondering why his team waited until they were 2-0 down before sparking into life.
Ferguson took off misfiring strikers Javier Hernandez and Dimitar Berbatov and sent on Gabriel Obertan and Macheda with his side looking beaten but they raised themselves for a late rally to earn a point that had appeared out of reach following the stirring efforts of Villa.
It was the sixth draw in seven Premier League outings for United on their travels this season and, although they kept up their unbeaten record for the campaign, they have now 12 points dropped away from home.
United had the motivation of knowing a win at Villa would close the gap to one point on league leaders Chelsea, who will be playing on Sunday, but the visitors lacked urgency.
They were almost caught napping early on when Barry Bannan slid a ball inside right-back Wes Brown to find Stewart Downing and it needed centre-back Rio Ferdinand to come across and clear out the danger.
United briefly threatened when Hernandez's pass released Berbatov but his early season confidence in front of goal was missing as the Bulgarian sidefooted disappointingly wide.
The visitors' lacklustre play was epitomised when a well-worked free-kick saw Nani play in Evra on the left only for his low whipped ball to fly across the Villa goalmouth without a team-mate showing a desire to get to it.

606: DEBATE We need a creative midfielder KingDeanWindass

United needed a player in the same mould as the suspended Paul Scholes, whose ability to spray the ball around and get forward from midfield was badly missed.
Hernandez and Berbatov were well-marshalled by a resolute and experienced Villa defence, but the rest of the home side was predominantly made up of up-and-coming talent and the more their opponents struggled the more they grew into their task.
Albrighton was a threat on the right flank, while the central midfield pairing of Bannan and Jonathan Hogg, the latter making his league debut, showed plenty of youthful zest.
Young had a half-volley saved by Edwin van der Sar and Downing saw a shot deflected narrowly wide off Ferdinand as the home side sensed United's fragility.
Not even a half-time teamtalk from Ferguson inspired United to positive action and they looked increasingly vulnerable after the break.
Albrighton sent a far post shot wide as Villa pressed and he then headed an inviting Downing cross across goal and wide.
A fleet-footed Villa full of energy and verve were piling on the pressure and United were rescued by the woodwork when Downing sent in another threatening ball from the left and Collins rose highest to launch a thunderous header against the crossbar.
United were rocking and when the ball broke loose after a Vidic tackle on Young, Agbonlahor crashed a shot off the United post.
Villa were finally rewarded when a counter-attack ended with Wes Brown felling Young, who picked himself up to score emphatically from the spot.
And it got even better for the home side after Macheda gave the ball away and a swift and clinical Villa break ended with Albrighton slotting in Downing's perfect cross to the far post.
But United are renowned for their ability to keep fighting until the final whistle and Macheda drilled in an 18-yard shot to give them a renewed belief.
When Vidic met a Nani cross at the far post and nodded in an angle header, the visitors suddenly felt victory was within reach.
Villa held on for a point but a home league win over United, last achieved in 1995, continues to elude them.