It was a deserved win at last for Fulham, who were perhaps out of sight after the hosts dominated a sluggish Spurs side in the first half before Richarlison equalized with his first goal of the season.
Fraser Forster made a great save just before the break to deny Rodrigo Muniz, who had a number of decent chances earlier.
Tottenham improved after the break and Manor Solomon almost scored a dream winner against his former club late on, but his curling effort from the edge of the box was saved.
Substitute James Maddison also hit a free-kick at the wall but a penalty was needed to settle the tie, with Fulham successfully converting all of them to send Spurs out.
It was a very encouraging performance overall from Fulham, whose manager Marco Silva had to watch from the stands after picking up three yellow cards in the first three Premier League games of the season.
Richarlison was relieved
Tottenham have made a good start to the season in the Premier League with a draw on opening day after back-to-back wins against Manchester United and Bournemouth.
As a result, this EFL Cup match has given Spurs boss Ange Postecoglou a chance to rotate his squad and impress others.
Richarlison was one of only two players – along with Van de Ven – to retain his place in the team since the 2-0 win over Bournemouth, and it was a chance for the Brazilian to finally leave his mark on the season as he sees it. To fill the void left by Harry Kane’s departure.
It looked like another chance would pass him by as he was largely anonymous in the first half, with a shot of note that was easily blocked by the Fulham defence.
But he showed his predatory instincts to nod home a fine cross from Ivan Perisic and, despite the defeat, Postecoglou will hope it gives him the confidence to score in the Premier League.