Louis van Gaal's side travelled to Birmingham on the back of six straight wins and boasting an excellent record at Villa, who had lost to Midlands rivals West Brom last time out.
However, United were frustrated by a dogged showing from Paul Lambert's men, who held on for a point despite playing the final 25 minutes a man down after Gabriel Agbonlahor was handed a straight red card.
Christian Benteke gave Villa the lead in the 18th minute as he curled home only his second goal of the campaign.
United initially laboured in their quest to level matters, but pulled level in the 53rd minute when Radamel Falcao headed in from close range.
Lee Mason's controversial decision to send off Agbonlahor for a foul on ex-Villa man Ashley Young 12 minutes later looked to have tilted the contest in United's favour, but the visitors - who introduced the fit-again Angel di Maria off the bench - could not find a winner.
United dominated possession in the opening stages but struggled to find a way through a well-organised Villa side.
Robin van Persie crafted the visitors' first chance as his 16th-minute volley forced Brad Guzan into a strong near-post save, but United were punished for their lack of threat in front of goal by a piece of brilliance from Benteke.
The Belgium striker controlled a left-wing free-kick from Fabian Delph - in as part of four changes by Lambert - with his chest before teasing Jonny Evans and curling an expertly placed strike into the top-left corner to leave David de Gea, making his 150th appearance for United, with no chance.
Villa's goal opened things up as United poured forward with greater intent and the visitors almost levelled when Guzan reacted late to parry away Young's cross-cum-shot.
Darren Fletcher - brought in by Van Gaal along with Falcao - was replaced by Tyler Blackett at the start of the second half, with Michael Carrick moving from defence to midfield.
United would have fallen further behind had De Gea not brilliantly tipped Benteke's header from a Delph corner over the bar.
Van Persie was then denied by Guzan at the other end, but the American could do nothing to prevent Falcao from restoring parity.
Young whipped in a left-wing delivery and the on-loan Monaco man made no mistake, using the power of the cross to head the ball beyond a helpless Guzan.
United were handed a further boost when Agbonlahor was dismissed for a seemingly innocuous challenge on Young, referee Mason displaying no hesitation in brandishing a red card despite an apparent lack of intent on the part of the Villa forward, who caught the shin of his former team-mate.
Jores Okore was then forced to clear Carrick's goal-bound header, with Villa clinging seemingly clinging on for a point.
Yet Leandro Bacuna almost snatched all three for the hosts with a fierce long-range drive that flew narrowly over the bar, and the fact that United failed to break down a depleted Villa outfit may give Van Gaal cause for concern over Christmas as United aim to cement a top-four berth.
