Davinson Sanchez saw his effort from 12 yards crucially saved by Marek Rodak as the hosts triumphed 5-3 on spot-kicks on a dramatic night at Craven Cottage to successfully book their place in the last 32 of the competition.
Kenny Tete slammed home the winning penalty for Fulham, who also notched in the shootout through Andreas Pereira, Raul Jimenez, Joao Palhinha and Harry Wilson.
Captain Heung-min Son and Dejan Kulusevski had both netted for Spurs before oft-maligned centre-back Sanchez’s miss as the surprise third taker, with James Maddison keeping them alive briefly before Tete’s decisive intervention.
Tuesday’s London derby had ended 1-1 after 90 minutes, with Richarlison heading in his first goal of the season after the interval to cancel out a first-half own goal by Micky van de Ven, a second in just four Tottenham appearances for the summer signing from Wolfsburg, forced by excellent work and a dangerous cross from Tom Cairney.
It is Spurs’ first competitive loss of the Ange Postecoglou and post-Harry Kane era, following a fine start to their Premier League campaign that has seen them take seven points from their first three matches under their new boss.
So many of the Australian’s back-up and fringe players missed a crucial chance to impress as Tottenham badly lacked first-half fluency after making no fewer than nine changes from Saturday’s 2-0 win over Bournemouth in the top-flight, indebted to a few smart stops from back-up goalkeeper Fraser Forster and an inaccurate close-range header from Jimenez deep into second-half stoppage time to get to penalties, as well as a let-off miss by Bobby De Cordova-Reid.
Questions will be asked of Postecoglou as to why he made quite so many changes as Spurs frittered away perhaps their biggest chance to end a 15-year run without a major trophy before the league’s top seven had even entered the fray.
But Tottenham did improve after the interval, with Rodak denying former Fulham loanee Manor Solomon a goal on his Cottage return late on and Pierre-Emile Hojbjerg also skewing a decent chance wide at 1-1.
For Fulham, who were without manager Marco Silva due to an early-season touchline ban following three yellow cards already accumulated in the league, it is another confidence boost after their 10 men achieved an unlikely draw away at title-chasing Arsenal on Saturday to bounce back from a heavy west London derby defeat by Brentford.
Tottenham will look to respond in similar fashion when they travel to face newly-promoted Burnley at Turf Moor on Saturday, while next up for Fulham is a daunting trip to the Etihad Stadium to take on defending champions Manchester City.