Paul Pogba scored the only goal of the game in the 71st minute when steering a Marcus Rashford cross through the legs of Nick Pope.
It was Burnley's fifth defeat on the bounce at home to the Red Devils and the 12th time in their last 13 meetings at Turf Moor where they'd failed to score.
Here are our RATINGS as Burnley's first league game of 2021 ends in defeat...
9. Ashley Westwood 6
Once again ran himself into the ground. United found it difficult to play their way through the middle, particularly in the first half, with Westwood offering a protective shield in front of the defence. Tiredness crept in, but continued to give his all.
10. Ashley Barnes 5
Considerably better and more effective in the first half than after the break. Caused problems when pinning and physically overpowering Wan-Bissaka and made a nuisance of himself. Dropped off in the second half.
11. Chris Wood 4
The striker seems to be struggling for confidence at the moment. He failed to affect the game in any way, shape or form, despite his best efforts, and was replaced after the break. Went close in the first half when his strike was deflected wide by Bailly.
12. Dwight McNeil 5
Should arguably have been introduced earlier with the Clarets crying out for a ball-carrier. Looked eager, shifting inside to get on the ball, and put the United defence under pressure with a collection of late balls into the box.