Scott Parker's third-placed side lined up for their return to action against the Bees sat seven points behind Championship front-runners Leeds and six adrift of second-placed West Brom.
Fourth-placed Brentford began the day four points behind Fulham and Thomas Frank's side were also dealt a blow in their preparations with the news that winger Bryan Mbeumo had tested positive for coronavirus.
But after a goalless first-half in which Fulham's Bobby Decordova-Reid hit the woodwork, Brentford struck twice in the closing stages with Said Benrahma firing the Bees ahead in the 88th minute before substitute Emiliano Marcondes added a second in the first minute of added time.
Marcondes had set up Brentford's first goal and while Fulham earlier had the ball in the net through Aleksandar Mitrovic, the Serbian striker was clearly offside.
The victory took Brentford to within one point of Fulham but Leeds can now move ten points clear in the automatic promotion spots with eight games left if winning at Cardiff on Sunday lunch-time.
United dropped down to second on goal difference after West Brom's goalless draw at home to Birmingham City on Saturday afternoon.