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.
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.