Ademola Lookman’s second-half strike was the difference between the two sides, although United should have had a late penalty when Fulham ‘keeper Alphonse Areola wiped out Jayden Bogle.
Not only did the goalkeeper escape punishment, he somehow won the free-kick from a challenge that left Blades boss Chris Wilder grateful that Bogle wasn’t seriously injured.
Here’s how our man rated United’s players at Craven Cottage.
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. Aaron Ramsdale 6
Had to be alert early on as a corner from the Fulham left drifted dangerously close to his goal, before he tipped it over. Looked comfortable until Lookman's shot beat him - but it was hit with remarkable power and he would have done well to see it, never mind save it Photo: Pool
. George Baldock 5
Did superbly to clear the ball off the line from Loftus-Cheek after he eventually found a way past Ramsdale. Booked for a foul on Lookman Photo: David Klein
. Ethan Ampadu 4
Probably felt dizzy by the end of the game after being switched between defence and midfield so many times. Too weak in the tackle again as Lookman burst through him and scored. Photo: Simon Bellis
. Phil Jagielka 5
Let no-one down after being wheeled out to replace the injured John Egan. Will he keep his place against Liverpool? Replaced by Bogle. Photo: Pool
2. Aaron Ramsdale 6
Had to be alert early on as a corner from the Fulham left drifted dangerously close to his goal, before he tipped it over. Looked comfortable until Lookman's shot beat him - but it was hit with remarkable power and he would have done well to see it, never mind save it Photo: Pool
3. George Baldock 5
Did superbly to clear the ball off the line from Loftus-Cheek after he eventually found a way past Ramsdale. Booked for a foul on Lookman Photo: David Klein
4. Ethan Ampadu 4
Probably felt dizzy by the end of the game after being switched between defence and midfield so many times. Too weak in the tackle again as Lookman burst through him and scored. Photo: Simon Bellis