Felix Magath’s improving side had won their two previous games and they reacted impressively after falling behind to a close-range Paulinho strike in the 35th minute, with Steve Sidwell equalising almost immediately.
However, second-half goals from Harry Kane and Younes Kaboul secured victory for Tim Sherwood’s Spurs, with Sidwell seeing a late penalty saved by Spurs goalkeeper Hugo Lloris.
Defeat left Fulham two points from safety, ahead of a home game with Hull City next weekend.
“If we had got any points here, it would have been an extra point for us,” said Fulham manager Magath.
“We have to win our home games and I think we can manage it.”
Sixth-place Spurs closed to within four points of the Champions League places, although they have played a game more than both fourth-place Arsenal and fifth-place Everton.
With leaders Liverpool not in action until Sunday, when they visit Norwich, Chelsea can provisionally take over at the top of the table if they win at home to bottom club Sunderland in Saturday’s late game.
Fulham slipped one place to 19th after Cardiff City moved above them on goal difference by drawing 1-1 at home to Stoke City.
Marko Arnautovic gave Stoke the lead from the penalty spot in first-half injury time after Kim Bo-kyung was contentiously adjudged to have tripped Peter Odemwingie.
However, Peter Whittingham equalised with a penalty of his own after Steven Nzonzi tripped Fraizer Campbell, and Cardiff might even have won, only for a Juan Cala effort to be ruled out for offside.
Elsewhere, an ice-cool stoppage-time penalty by Wilfried Bony gave Swansea City a 2-1 victory at Newcastle United that took the Welsh club six points clear of the relegation zone.
Bony had earlier scored with a header to cancel out Shola Ameobi’s 23rd-minute opener for the home side.
Aston Villa spurned a chance to put clear daylight between themselves and the bottom three after being held to a 0-0 draw at home to Southampton that left Paul Lambert’s side five points above the drop zone.
In the day’s other fixture, a 59th-minute Mile Jedinak penalty saw Crystal Palace win 1-0 at West Ham United, completing a sequence of five successive top-flight wins for the first time since December 1992.
Aston Villa 0 Southampton 0
Cardiff 1 (Whittingham 51-pen) Stoke 1 (Arnautovic 45-pen)
Newcastle 1 (Ameobi 23) Swansea 2 (Bony 45, 90-pen)
Tottenham 3 (Paulinho 35, Kane 48, Kaboul 62) Fulham 1 (Sidwell 37)
West Ham 0 Crystal Palace 1 (Jedinak 59-pen)
Chelsea v Sunderland (1630GMT)
Everton v Manchester United (1510 GMT), Hull v Arsenal (1305GMT), Norwich v Liverpool (1100GMT)
Manchester City v West Brom (1900GMT)