Successive wins against Aston Villa and Norwich City had lifted Felix Magath's men to within touching distance of safety prior to this weekend, but an inability to defend set-pieces proved costly as Fulham failed to make it three victories in a row.
Tottenham's first and third goals arrived from Christian Eriksen free-kicks, with Paulinho and Younes Kaboul converting from close range on each occasion.
Paulinho's 35th-minute opener was cancelled out by Steve Sidwell almost immediately.
However, Harry Kane registered his third goal in as many games to restore the home side's advantage early in the second half before Kaboul capitalised on more poor defending just after the hour mark.
Sidwell had a chance to pull one back with 13 minutes remaining, but his penalty was saved by Hugo Lloris.
Fulham remain two points behind fourth-bottom Norwich, who host league leaders Liverpool on Sunday, while Tottenham, in sixth, will retain slim hopes of qualifying for the UEFA Champions League.
Tim Sherwood, who admitted prior to the game that he "could not tell you the best 11 players at Tottenham", selected Ezekiel Fryers in place of Vlad Chiriches at centre-half, yet there was no place for Sandro, with the midfielder taking to Twitter to confirm he was not injured.
Scott Parker returned to face one of his former clubs as Fulham made five changes from the win over Norwich, but loanee Lewis Holtby was ineligible.
The visitors started brightly, with Hugo Rodallega – scorer of the winning goals against Villa and Norwich – a lively presence in attack.
Tottenham goalkeeper Lloris dashed from his line to deny Rodallega from close range during an opening half-hour that saw Fulham operate with confidence.
However, after David Stockdale had pulled off a fine save at the other end – tipping a volley from Aaron Lennon on to his left-hand post, it was Tottenham who took the lead.
Eriksen's delightful free-kick from the right was allowed to run all the way through to Paulinho, leaving the Brazilian with the simplest of finishes from barely two yards.
To their credit, Fulham responded almost immediately. Fryers was unable to effectively clear a pass from Sidwell, who continued his run and jinked into the penalty area before finishing calmly.
Tottenham moved back ahead after the break when Lennon was allowed time to deliver a cross and Kane rose to beat Stockdale with a glancing header.
Within three minutes, Lloris pulled off an acrobatic stop to prevent another swift equaliser after Rodallega had met a cross from John Arne Riise with a powerful header.
Fulham were soon left to rue the missed opportunity as John Heitinga brought down Danny Rose and Kaboul got on the end of Eriksen's resulting free-kick.
Eriksen was then penalised for handball to provide Sidwell with an opportunity from the spot, but Lloris dived to his right to maintain Tottenham's two-goal cushion.
The hosts had few problems thereafter in securing only a third win in nine games across all competitions, leaving Fulham to face another week in the relegation zone.
