Leading through Harry Kane's first-half header, Spurs' attempts to protect their only invited more pressure from the visitors, who grew in confidence as the game wore on.
And their pressure told in the 74th minute as Ivan Cavaleiro headed brilliantly home to move Scott Parker's side within two points of safety with two games in hand on 17th-placed Brighton.
So who were the best and worst players on the pitch?
✔️ GOOD PERFORMANCE
Ademola Lookman: 6.5
His 23 minutes on the pitch weren't quite enough to earn Ademola Lookman a truly great rating, but his impact shouldn't be underestimated.
Spurs simply couldn't handle the Englishman's direct running, or the vision that led to seven final third passes in a short cameo.
One of those included a truly brilliant cross for Cavaleiro's deserved headed equaliser.
❌ BAD PERFORMANCE
Eric Dier: 6.6
Jose Mourinho made his name as a coach happy to grind out 1-0 wins, and his team's approach after taking the lead looked geared toward such a result.
However, you need a solid defence to earn one-goal victories, and this Spurs backline is nowhere those previously put together by this manager.
Eric Dier somewhat typified the issues facing the Portuguese, winning just four out of 11 duels, including only half of his eight aerial challenges.
⭐ STAR MAN
Alphonse Areola: 7.2
Fulham probably knew that they were going to need their goalkeeper to play well if they were take anything from this trip across London.
And Areola certainly did that, keeping his team in the game almost singlehandedly at times during periods of Spurs domination.
The Frenchman made five saves and dealt with a number of crosses impressively as the hosts took to aerial bombardment in search of a winner.