The 17-year-old substitute, who replaced Nani after 61 minutes, showed tremendous composure to turn Villa defender Luke Young and curl the ball past Villa keeper Brad Friedel and give the champions the victory that took them back to the top of the table.
United have 68 points from 30 matches. They are one point ahead, with a game in hand, of Liverpool who had gone top on Saturday after an equally late and dramatic winner from Yossi Benayoun in their 1-0 win at Fulham.
Chelsea, who won 2-0 at Newcastle United on Saturday, are third with 64 points from 31 games.
United, with Rio Ferdinand and Dimitar Berbatov injured and Paul Scholes, Nemanja Vidic and Wayne Rooney all suspended, had lost their previous two league games to Liverpool and Fulham and looked to be heading for their third successive defeat with only 10 minutes to go.
Villa, looking for their first win in nine matches and first at Old Trafford since 1983, led 2-1 but the game turned against them and left them hanging on to fifth place by a point from Everton, 4-0 winners at home to Wigan Athletic.
FERGUSON GAMBLE
Although Villa made the brighter start, United took the lead with a 14th minute Cristiano Ronaldo goal following a free kick awarded for a James Milner back pass to Friedel.
Villa struck back with headers from John Carew after 30 minutes and Gabriel Agbonlahor after 58 as they dominated the aerial challenges against Gary Neville, playing in the unfamiliar role of centre-back.
United regained their early dominance when Macheda came on and Ronaldo brought them back into the game with his second goal to make it 2-2 with a low shot from the edge of the box.
Ferguson said he took a gamble on his defensive formation.
"I did take a gamble in that respect," he told Sky Sports News.
"Gary hasn't played for two months and if I played him at right back it was asking a lot of him at 34 years of age...
"So I thought I'd start him at centre-half and see how he coped with that but of course Carew is ... a massive man (1.93 metres).
"The best move I made was putting John O'Shea back to central defence, that helped win the match for us because he was marvellous and Gary, at right back, got better and better."
Villa manager Martin O'Neill told Sky Sports his team played superbly and did not deserve to lose.
"It's all very well being involved in another fantastic game, a really, really incredible game, but we've been beaten and we didn't deserve to be beaten."
Everton crushed Wigan at Goodison Park with two goals from Jo and one each from Marouanne Fellaini and Leon Osman.
