Substitute Ole Gunnar Solskjaer sneaked a late winner to ensure opening goalscorer Henrik Larsson enjoyed a dream debut for Manchester United.
Larsson scored his first goal in Man Utd colours against Villa
Larsson capped a fine display when he volleyed in on 55 minutes to score in his first FA Cup tie.
United almost doubled their lead when Ryan Giggs' free-kick hit the bar before substitute Milan Baros equalised when he slid a low shot in the corner.
Solskjaer had the final say when a tame shot embarrassed keeper Gabor Kiraly.
It was tough on Villa, who battled bravely and soaked up intense United pressure.
After a lethargic opening, United began to up their tempo and the movement of Larsson and Wayne Rooney started to cause Villa problems.
A sublime one-two led to Larsson flicking a return volley into Rooney's path but the England forward shot tamely at the keeper.
However, that effort proved to be one of Rooney's best in a first half where his touch often deserted him in the box and his shots from distance were slashed high and wide.
Yet when Rooney did produce the kind of effort expected of him, swivelling and stabbing a shot at the near post after sparkling wing work from Cristiano Ronaldo, Kiraly made a smart save.
And there was better to come from Kiraly, who superbly diverted a low shot from Larsson after the Swede had been played through by Michael Carrick.
Moments before, Larsson had been the provider when he unselfishly squared the ball to Rooney, who wasted the chance by hesitating and allowing Wilfred Bouma to make a challenge.
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It typified stubborn Villa defending, although United's profligate finishing contributed to the deadlock remaining intact.
While the visitors soaked up the pressure, they carried very little attacking threat of their own - a Gareth Barry free-kick that curled over the bar was their only shot of note in the opening half.
That clearly had not been lost on manager Martin O'Neill, who waited only seven minutes after the break before replacing striker Juan Pablo Angel with Baros.
However, two minutes later Larsson - who used to play under O'Neill at Celtic - made the breakthrough.
After collecting Rooney's pass on the edge of the area, Larsson flipped up the ball with one touch and with his second, lashed a volley into the top corner.
The goal should have led to United assuming full control and had Giggs' free-kick hit the bar and gone in rather than over, the contest would have been finished.
But somehow, Villa dragged themselves back in contention and for the first time in the match began to create chances.
Gary Cahill almost levelled the score when he shaved the post with a header after connecting with Gavin McCann's corner.
And shortly afterwards, Barry's precise pass found Isaiah Osbourne but his effort was well saved by Tomasz Kuszczak.
Villa may have felt they had wasted their best chance but then Cahill's shot was trapped by Baros, who coolly slid the ball into the bottom left corner.
However, the drama was not over as Solskjaer prevented the replay Villa arguably deserved when he shot from the right and the ball squirmed underneath the unfortunate Kiraly.
Man Utd: Kuszczak, Neville, Ferdinand, Brown, Evra, Ronaldo, Carrick (O'Shea 89), Giggs, Park (Fletcher 72), Rooney, Larsson (Solskjaer 78).
Subs Not Used: Van der Sar, Heinze.
Goals: Larsson 55, Solskjaer 90.
Aston Villa: Kiraly, Hughes, Ridgewell, Cahill, Bouma, McCann, Osbourne, Petrov (Samuel 66), Barry, Angel (Baros 53), Agbonlahor.
Subs Not Used: Davis, Whittingham, Olejnik.
Goals: Baros 74.
Ref: M Atkinson (W Yorkshire).