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United lead the table with 68 points from 30 matches, one point more than Liverpool who had gone top on Saturday after their 1-0 stoppage time win at Fulham.
United seemed to be heading for a third straight league defeat before Cristiano Ronaldo equalised after 80 minutes.
He had also given United the lead after 14 minutes following a free kick awarded for a back pass.
In between those two goals, Aston Villa scored twice with headers from John Carew after 30 minutes and Gabriel Agbonlahor after 58.
In the day's other game, Everton crushed Wigan Athletic 4-0 at Goodison Park with two goals from Jo, and one each from Marouanne Fellaini and Leon Osman.
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