Fulham and Sunderland could not be separated at Craven Cottage so they will battle it out in a FA Cup fourth round replay next month.
Ex-Tottenham player Jack Clarke capitalised on a defensive error to fire Sunderland in front early on.
This sparked Fulham into life and Tom Cairney netted with a low shot to make it 1-1 with around half an hour to go.
While neither side will have wanted to add to their already congested fixture schedule, they will now have to face each other again to decide which team will progress to the fifth round of the competition.
Fulham started the game on the front foot as they looked to return to winning ways following successive 1-0 defeats to Tottenham and Newcastle.
Manager Marco Silva made seven changes to his starting XI, but it was Sunderland who took an early lead.
Clarke capitalised on a mistake from Issa Diop, taking the ball off the Fulham defender before running in on goal and slotting past Marek Rodak.
Fulham almost equalised in the 14th minute but Tosin Adarabioyo’s header from an Andreas Pereira cross bounced into the ground and over goalkeeper Anthony Patterson and the crossbar.
Ross Stewart was then carried off the field on a stretcher with what appeared to be an ankle problem, forcing Sunderland into their first substitution of the game and denying him the chance of adding to his tally of 10 goals in 13 games this season.
Fulham had another good chance on the stroke of half time from a quick run down the left wing from Manor Solomon, who pulled the ball back to Pereira but his shot was expertly blocked on the line by Daniel Ballard.
Harry Wilson also had an opportunity for the hosts when he was picked out by Cairney on the right hand side, cutting inside to create space to shoot and forcing Patterson into a good save.
Patterson denied Wilson again minutes later when he came off his line to close the angle for the Fulham winger.
Sunderland almost doubled their lead when they caught Fulham on the break, with Patrick Roberts winning the ball, running through most of the home side’s half before taking a shot, which was just wide of Rodak’s goal.
However, Fulham eventually levelled from a clever piece of individual skill from Cairney just after the hour mark.
The midfielder was picked out by Layvin Kurzawa in the box but still had a lot of work to do, weaving his way past two defenders to create space before firing past Patterson.
Silva brought on Aleksandar Mitrovic and Willian in an attempt to force a finish, and Fulham’s leading goalscorer did send a header straight at Patterson from a Kenny Tete cross.
Sunderland thought they had scored the winner when 15-year-old Christopher Rigg had the ball in the back of the net in the 90th minute, but the goal was rightly ruled out for offside to ensure a replay will be needed at the Stadium of Light.
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