Emmanuel Adebayor got Spurs off to a dream start when he opened the scoring in only the second minute before Jermain Defoe doubled their lead soon after the hour mark, but the Lilywhites were unable to secure the final automatic Champions League place after local rivals Arsenal won 3-2 at West Bromwich Albion.
Spurs are still waiting to finish above their neighbours in the table for the first time since 1995. They last finished third 22 years ago.
Tottenham can still return to Europe's top competition after a one-year absence if Bayern Munich beat Chelsea to win the Champions League final on Saturday. Should Chelsea win the trophy for the first time, Spurs will be robbed of their place in the play-offs for next season's competition and will have to make do with the Europa League.
Defeat for Fulham denied them the chance to finish seventh, which would have been their highest ever Premier League final position.
Tensions were understandably high before the game as Spurs opted to field an unfamiliar 4-2-3-1 formation, with Jake Livermore replacing the suspended Danny Rose and winger Gareth Bale moving to left-back.
But nerves were soon settled in North London when Adebayor cut in from the left, played a slick one-two with Rafael van der Vaart and calmly finished into the far bottom corner with just 94 seconds on the clock. The goal was the Togo striker's 17th in the league of his impressive one-year loan spell at Spurs, and was also the quickest goal scored by them since Defoe’s first-minute strike against Manchester United in September 2009.
The buoyant atmosphere in N17 was greatly augmented when news filtered through that Arsenal were losing 2-1 at The Hawthorns having taken a lead almost as early as Tottenham's, but the home crowd endured a few frights of their own before they got to half-time with their lead intact.
Just as when Tottenham won 3-1 in the reverse fixture back in November, veteran goalkeeper Brad Friedel was called upon to make some vital saves as Fulham enjoyed some good attacking spells despite missing top scorer Clint Dempsey through injury.
Norwegian left-back John Arne Riise was allowed to make a typically powerful surge forward through the middle, and his strike was parried by Friedel before Bale hooked away the rebound.
Soon afterwards the American keeper was called into action again. This time it was Belgian forward Moussa Dembele – often linked with a move to Spurs – whose low strike from range was saved. William Gallas had to use all his strength to muscle his way in front of Pavel Pogrebnyak and deny the big Russian striker a simple tap in.
Just before the break, Kyle Walker limped away from a collision with Dembele in which the Fulham man inadvertently landed on his foot, and soon after the restart the recently-crowned PFA Player of the Year was replaced by Ryan Nelsen. Walker would later re-emerge from the tunnel on crutches, putting his participation at Euro 2012 in serious doubt.
An eerie quiet descended upon the ground as the news that Laurent Koscielny had put Arsenal back in front filtered in, and that sense of trepidation was compounded when Dembele drilled a rasping shot off the foot of the far post.
Spurs manager Harry Redknapp responded by bringing on Defoe on the hour mark in place of Van der Vaart, and he took less than three minutes to make an impact. Aaron Lennon's shot was deflected into the path of the tiny striker, who pounced to finish for his 11th league goal of the season and fourth from the bench.
Fulham had not scored in six of their previous seven league visits to White Hart Lane, including each of the last three, and they were once again denied when Friedel tipped Dembele's strike from range over the bar in the final moments of normal time.
With a nod to the club's future, Redknapp brought on 21-year-old defender Adam Smith for his first-team debut as Younes Kaboul limped off with a quarter of an hour remaining. However, Spurs fans will not be able to look further ahead than the coming Saturday, when their team's fate will be inextricably linked to that of their London rivals in Munich.