The meeting, held at the Turf Moore stadium in Burnley, ended with a score of 1: 0 in favor of the guests.
The victory for Manchester United was brought by the goal of Paul Pogba, who scored in the 71st minute with the transfer of Marcus Rashford.
This result allowed Manchester United to lead the Premier League standings with 36 points.
Burnley, with 16 points, is in 16th place.
In a parallel match, Liverpool's Everton beat Wolverhamton Wanderers 2-1 away.
Earlier it was reported that Sheffield won their first Premier League win of the current season, beating Newcastle.