United took the lead after 19 minutes, thanks to a bullet header from Casemiro, who converted Bruno Fernandes’s free-kick.
The Reds doubled our advantage 11 minutes into the second-half through Cunha, who was restored to the line-up following the injury to Patrick Chinazaekpere Dorgu.
Fulham looked to have a rescued a point with two goals in six second-half minutes. Raul Jimenez converted a penalty, before Kevin equalised for the visitors, moments into stoppage time.
However, United responded through substitute Benjamin Sesko, four minutes into added time, to spark jubilant scenes inside Old Trafford.
FIRST HALF- CASEMIRO HEADS UNITED IN FRONT
Manchester United were the first side to threaten, with Amad stinging the palms of Bernd Leno through a powerful shot from the edge of the box.