Harry Kane's brilliant header was not enough for Tottenham as Jose Mourinho's side were pegged back to a 1-1 draw by Ivan Cavaleiro's equally fine effort.
Spurs looked set to claim back-to-back Premier League victories for the first time since November thanks to Kane's 25th-minute effort – his 36th league goal against a London rival.
Scott Parker was enraged by the decision to reschedule his team's trip to Tottenham Hotspur Stadium at such short notice, but Fulham stayed in the game and, with Son Heung-min squandering a great chance to wrap things up, got their reward.
Substitute Ademola Lookman proved the difference-maker as he pinged in a cross that was met by the towering Cavaleiro to seal a share of the spoils.
Sergio Reguilon blazed over inside the opening 10 minutes, but Fulham showed plenty of intent and Hugo Lloris had his palms stung by Andre-Frank Zambo Anguissa's strike.
Alphonse Areola came to the fore with two superb stops, both from Son, who prodded goalwards from point-blank range before attempting to guide a header into the top-right corner.
Areola was beaten in the 25th minute, though. Where Son went for height, Kane went low, diving to meet Reguilon's exquisite left-wing cross and head in off the post.
Kane was the beneficiary of another terrific cross – this time from Serge Aurier – soon after, but failed to keep his header down.
Tosin Adarabioyo made a fantastic last-ditch tackle to frustrate Moussa Sissoko after the restart, while Areola had to lunge across to keep out Harry Winks' dipping effort.
Son could have wrapped things up with just under 20 minutes remaining, yet hit the base of the right-hand upright, and Spurs were made to pay.
Cavaleiro towered over Eric Dier to meet Lookman's cross and send a powerful header beyond Lloris, rescuing a hard-earned point with Fulham's first shot on target of the half, with Reguilon rightly denied a last-gasp winner by the offside flag.
What does it mean? Fulham taking it point by point, but Spurs frustrated
Mourinho's team had just five shots after the break, in contrast to Fulham's eight, and questions might again be raised over a lack of ambition or ability to kill games off.
Fulham have now drawn their last five league games to move within two points of safety, while Spurs sit sixth, two points behind Everton, Manchester City and Leicester City.
Kane clinical but Son found wanting
Son and Kane's near-telepathic partnership has been integral to Tottenham's form, and the latter – who has now scored 25 top-flight goals with his head, left foot and right foot – has steadily racked up the goals, and is on 11 in the Premier League for the campaign.
That is one behind Son, who missed three gilt-edged opportunities, including that crucial one-on-one just prior to Fulham's equaliser.
Lookman sparks the comeback
Bar an infamous Panenka attempt against West Ham that cost Fulham a point, Lookman has been extremely impressive since joining on loan from RB Leipzig.
His introduction from the bench in the 67th minute injected fresh impetus into the visitors, and the 23-year-old created three chances during his cameo, more than any other Fulham player and fewer than only Serge Aurier (four) in the game.
Sheffield United picked up their first league win of the season against Newcastle United on Tuesday, and they host Spurs on Sunday, while Fulham face Chelsea a day earlier.