Wolves missed three penalties to hand Tottenham a 3-2 shoot-out victory following a 2-2 draw in Wednesday's EFL Cup third-round clash.
Tanguy Ndombele and Harry Kane fired Tottenham into a two-goal lead inside 23 minutes but Leander Dendoncker responded for Bruno Lage's men before the interval.
Daniel Podence levelled things up 13 minutes after the break following a mistake from Ndombele, but penalties were required at Molineux as neither side could find a late winner.
Pierluigi Gollini managed to save from Dendoncker and with both Conor Coady and Ruben Neves faltering, Spurs marched into the fourth round despite Pierre-Emile Hjobjerg missing.
Into the hat for the fourth round! pic.twitter.com/d0UZf7ILJw— Tottenham Hotspur (@SpursOfficial) September 22, 2021
Ndombele opened the scoring with 14 minutes gone, getting the better of Coady before drifting inside Willy Boly and slotting through John Ruddy's legs.
The visitors doubled their advantage nine minutes later, with Dele Alli carving open the Wolves defence before Kane drilled into the bottom-left corner.
However, Dendoncker halved Spurs' lead as he climbed the highest from Rayan Ait Nouri's outswinging corner to head into the top-right corner.
Alli and Kane attempted to link-up once more after half-time, but Ruddy was on hand to deny the former before Ndombele was at fault for Wolves' equaliser.
The France midfielder was caught in possession by Hwang Hee-chan, with Dendoncker subsequently finding Podence, who curled into the bottom-right corner to level.
Kane's header almost restored Spurs' lead but Ruddy's reflex save kept the scores level before Neves' deflected strike clipped the crossbar as the tie headed towards penalties.
Neves blasted over the fifth spot-kick after the first four had all converted before Dendoncker saw his low effort saved by the Spurs goalkeeper diving to his right.
Hojbjerg could have won it for the visitors but Ruddy denied the Denmark midfielder. However, that did not matter as Coady smashed into the crossbar to hand the away side their place in the fourth round.
What does it mean? Nuno secures bragging rights again
Spurs defeated Wolves 1-0 in August on Nuno Espirito Santo's first return to Molineux and the Portuguese head coach inflicted further damage again on Wednesday.
He will have been worried about throwing away a two-goal lead but that did not matter as the visitors made it into the fourth round for the eighth time in their last 10 attempts.
Meanwhile, Wolves have now lost consecutive EFL Cup home games for the first time since a run of three defeats between September 1998 and August 2000.
Cristian Romero managed a team-high 46 passes as he produced an assured performance alongside Davinson Sanchez.
The centre-back also won a team-leading 71.4 per cent of his duels and made the most interceptions of any player on the pitch.
Fabio Silva needlessly collected a first-half yellow card for a late tackle on Japhet Tanganga in what was a frustrating showing.
The youngster disappointed and was hooked off at half-time after missing a glorious opportunity, completing just six passes and winning only one of his five duels.
Tottenham make the short trip to fierce rivals Arsenal on Sunday in the Premier League, while Wolves travel to Southampton on the same day.