The meeting, held at the Craven Cottage stadium in London, ended with a score of 2: 1 in favor of the guests.
Edinson Cavani and Paul Pogba scored for Manchester United.
The only goal of the hosts on the account of Ademola Lukman.
Manchester United lead the Premier League standings with 41 points.
Fulham are in 18th place with 12 points.
Earlier, Manchester City beat Aston Villa in the Premier League match.