Tony Mowbray’s side took an early lead when Jack Clarke took the ball off defender Issa Diop before beating goalkeeper Marek Rodak with a low finish.
Sunderland were then dealt a big injury blow when top scorer Ross Stewart was stretchered off with an injury in the first half.
Fulham’s equaliser came just after the hour mark as captain Tom Cairney beat two opposition players before converting his shot to force a replay.
Here’s how Phil Smith rated the Sunderland players at Craven Cottage:
Fulham’s equaliser came just after the hour mark as captain Tom Cairney beat two opposition players before converting his shot to force a replay.
9. Jack Clarke - 7
Took his goal well having sensed the moment to press and steal the ball. Got into some good areas and looked out on his feet by the time he was replaced with just over ten minutes to go. 7 Photo: Martin Swinney
10. Ross Stewart - 6
Started brightly and got involved in some nice moves before suffering what appeared to be a serious injury when chasing a loose ball. Was stretchered off in serious discomfort - a major worry for Sunderland to put it mildly. 6 Photo: Frank Reid
11. Abdoullah Ba (sub) - 6
Moved the ball well and got into some good areas, just lacked that final touch on one or two occasions. Not overawed, though. 6 Photo: Frank Reid
12. Niall Huggins (sub) - 6
Steady in his defensive work after another injury issue. Did OK in possession and a very timely return to boost Mowbray’s options. 6 Photo: FRANK REID