Antonio Valencia was brought on in his place, with Nani pushed up front alongside Wayne Rooney, and Villa had no answer to the pace, movement and skill of the new-look front three.
So it was no surprise when Jones put the visitors in front.
Playing in midfield, the versatile 19-year-old timed his run into the box to perfection to confidently stroke home Nani's nicely-flighted cross.
Did you know?
The attendance of 40,053 was the highest at Villa Park this season
The chances kept coming with Given making a good save from Nani's header and Valencia's 35-yard shot sailing just over as United tried to turn the screw.
The game's injury jinx struck again when Given was taken off with a hamstring injury as the problems piled up for the shot-shy Villans.
After being booed off at half-time, the hosts were brighter in the second half and Emile Heskey should have done better when he headed over the bar from three yards out after Richard Dunne had steered the ball towards goal from a corner.
It was a poor finish, symptomatic of the problems faced by the Midlanders since the goals have dried up in recent weeks.
Alex McLeish left winger Charles N'Zogbia out of his starting line-up because of a breach of club discipline, but the home side could have done with the sort of spark their £9.5m summer signing can provide.
There was plenty of industry from Barry Bannan, Marc Albrighton and Jenas, but very little in the way of flair.
McLeish bemoans poor Villa passing
Lindegaard was making only his fifth appearance of the season in the United goal, with Ferguson opting to rest David de Gea, and the Dane was rarely troubled on his way to a third successive Premier League clean sheet of the campaign.
He did, however, make a fantastic fingertip save from a James Collins header with 15 minutes remaining.
Rooney, who pulled the strings for United alongside Nani and Jones, might have sealed victory when he blazed over with just three minutes remaining.
But United closed out the match without any further alarms to stay within striking distance of Roberto Mancini's pacesetters.
The performance of Jones, in particular, was significant for the Red Devils with England manager Fabio Capello's assertion that the teenager can be a star in both defence and midfield looking to be a fairly sound judgement.
Manchester United manager Sir Alex Ferguson:
Phil Jones took his goal very well. It was a good time to score and it settled us down.
It was a solid performance and winning away from home in the Premier League is never easy.
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