The Clarets brought back Ashley Barnes and Jeff Hendrick but the headline news came from United who made four changes and did not include Paul Pogba in their squad.
A scrappy opening period of the game was shaded by the visitors, Nick Pope having his palms stung on a couple of occasions but neither side truly took control.
0-0 seemed the likely outcome heading into the break but that changed on 44 minutes when Andreas Pereira made the most of an error by Charlie Taylor.
The midfielder found Anthony Martial and the Frenchman had no issues in slotting under the advancing Pope to break the deadlock.
Substitute Joe Hart was sent out to warm up at the break after Burnley’s number one had been seen struggling with an apparent ankle injury during the opening 45 but he returned from the interval and was forced into an early save by Daniel James.
For all they tried, Burnley struggled to get a foothold in the game, introducing the likes of Robbie Brady and Johann Berg Gudmundsson from the bench but to no avail.
United continued to strangle the game and as the hosts pushed, exploited the space, grabbing a second through Marcus Rashford in stoppage time.
There was a touch of fortune about the goal, the ball finding the England man in space in the box and as he slipped, he somehow diverted home.
The result lifts United up to fifth in the table ahead of their New Year’s Day clash at Arsenal, while the Clarets are 13th as they prepare to host struggling Aston Villa.