Rooney inspired United after coming on as substitute with 20 minutes left.
He fired just over seconds before Cristiano Ronaldo turned home Ryan Giggs' cross with nine minutes left.
Rooney then provided a superb finish with a minute left, firing across Scott Carson from 20 yards as United sealed a place in the FA Cup fourth round.
This was the fourth time in the past seven seasons Villa have been paired with United at the third round stage - and they have lost each time.
Nine players eligible to play for England were included in the two starting line-ups as Capello took his seat alongside the Football Association's chief executive Brian Barwick in the stands at Villa Park.
Rooney was not on display from the start in front of Capello, being kept on the bench after missing two games with a virus, but he had a massive impact when he finally emerged.
There was little for impassive new England coach Capello to get excited about in a poor first 45 minutes.
Giggs had the best chance on the stroke of half-time, when Villa keeper Carson palmed out Ronaldo's shot and the veteran star could only steer the rebound wide.
Rooney indulged in a lengthy warm-up routine at the start of the second-half, much to the delight of United's travelling fans.
United almost broke the deadlock without him after 56 minutes when Nemanja Vidic glanced Giggs' corner just off target via a deflection.
Villa made the first change seven minutes later, sending on Luke Moore for John Carew, who looked to be struggling for fitness throughout.
Rooney was finally introduced with 20 minutes left of what had been a dismal encounter, replacing Ji-Sung Park.
Villa occasionally posed a threat when they broke on United, but Ashley Young shot wastefully wide from 20 yards.
Rooney had a glorious chance to open the scoring after 79 minutes when he played a long pass to Ronaldo before taking the return and firing over the top.
But United did not have to wait long to take the lead, Ronaldo scoring seconds later.
Giggs' cross went through Curtis Davies' legs and Ronaldo forced his way in front of the flat-footed Wilfred Bouma to score.
Carson then made a fine double save from Michael Carrick as United threatened to hit Villa again on the break.
And Rooney completed a brilliant cameo with a low drive beyond Carson as United sealed the win.