In a hard-fought game, Paul Pogba showed sublime technique with a volley, which took a slight yet telling deflection off Matt Lowton to beat Nick Pope for the only goal of the game.
Manchester United were definitely the better team on the night and fully merited the three points. The win sent them top of the Premier League, three points clear of defending champions Liverpool, where they travel to this weekend..
On that note, here are five major talking points from this game.
#1 Manchester United start slow again
Once again, Manchester United weren't really at their best in the opening exchanges of an away league game. They were sloppy in possession and conceded a few too many free-kicks.
In fact, straight after kick-off, Robbie Brady had the game's first shot, just 14 seconds after the opening whistle. Manchester United survived the scare, as Burnley failed to conjure any clear-cut openings in the opening minutes.
The visitors sparked to life at around the half-hour mark and didn't look back from there. They dominated the ball, moved it around at a decent pace and created decent chances as well to go three points clear at the top.
#2 More VAR drama
Robbie Brady could have been sent off in the first half, as the VAR official deemed his challenge on Edinson Cavani to be a denial of a clear goal-scoring opportunity.
However, Brady got away when it was ruled that Luke Shaw had fouled Johann Berg Gudmundsson in the build-up.
In truth, Shaw's challenge was not the worst, but he followed through high on Gudmundsson after initially getting the ball anyway.
A few minutes later, Manchester United also had a goal ruled out after Harry Maguire planted a superb header in at the back-post. However, the Manchester United captain was ruled to be jumping on the back of Erik Pieters, and Burnley were awarded a free-kick.
There was also a minor check late in the game for a Maguire handball that could have given Burnley a penalty. However, that was deemed not to be a clear and obvious error by the officials.