It was a frustrating afternoon for the Black Cats, who missed a glorious chance to take the lead early in the second half before Raul Jimenez broke the deadlock for the visitors.
Jimenez then doubled his lead from the spot soon after, but the penalty award infuriated many Sunderland supporters.
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Brian Brobbey was penalised for pulling the shirt of Fulham defender Calvin Bassey, who went to ground in the area.
Referee Craig Pawson initially waved away the claims but his decision was overturned after VAR review.
A statement released by the Premier League said: “After VAR review, the referee overturned the original decision of no penalty to Fulham.
“Referee announcement: “After review, Sunderland 9 commits a holding offence on his opponent. Final decision is a penalty kick to Fulham and a yellow card to Sunderland 9.”
It wasn't so much the foul that infuriated Sunderland fans but the fact Bassey appeared to be marginally offside when the free-kick was swung in.
However, Bassey's offside position isn't relevant when it comes to the awarding of the penalty. That's because the foul took place before the offside offence was committed - or, more to the point, before the defender was deemed to be interfering with play.
That's why Bassey's offside decision wasn't part of the thinking when the goal was checked.
Enzo Le Fee later scored from the spot after Sunderland won a penalty when Dan Ballard was fouled, but Alex Iwobi wrapped up the points for Fulham.
Sunderland are next in action when they travel to Bournemouth next Saturday.