Tanguy Ndombele and Harry Kane gave the visitors the perfect start within 23 minutes before Leander Dendoncker got Wolves back in it before half-time.
Daniel Podence’s second half strike forced a penalty shoot-out but misses from Ruben Neves, Dendoncker and Conor Coady saw Wolves fall in round three.
Bruno Lage made nine changes to his side following the 2-0 defeat to Brentford at the weekend, but stuck with the 3-4-3 formation.
Only Max Kilman and Neves kept their place in the side as Willy Boly and Yerson Mosquera got their first minutes of the season. The latter was also making his competitive Wolves debut.
Hwang Hee-chan also got his first start in a Wolves shirt, starting in a front three of Podence and Fabio Silva. Lage named a strong bench that included striker Raul Jimenez and Adama Traore.
Jose Sa was not involved in the squad as John Ruddy started in goal and youngster Louie Moulden made the bench.
Returning former boss Nuno Espirito Santo made six chances to his side, starting in a 4-3-3 formation.
He still named a strong team, however, with star forward Kane leading the line. Former Wolves defender Matt Doherty only made the bench.
It was a lively start to the game with both sides eager to get on the ball and attack at will, but only six minutes in, Mosquera went down with an injury and needed medical assistance for three minutes on the field.
The young defender was stretchered off and left the field with his head in his hands as his debut was cut drastically short. Captain Coady replaced him.
Only minutes later, Coady was involved as Spurs took the lead. Podence won the ball back in midfield but played a short and poor pass to Coady who attempted to clear the ball first time, but instead smashed it off Ndombele. The midfielder carried the ball forward, turned Boly in the box and finished low beyond Ruddy.
From there Wolves did not improve. Sloppy passes and poor possession retention frustrated the home crowd and less than 10 minutes after the first goal Spurs added a second. Neves lost the ball in midfield and Dele Alli played a ball through the heart of the Wolves defence for Kane who slotted home.
From a Wolves corner, in which Dendoncker had a header saved, Spurs broke forward and should have made it three when Giovani Lo Celso turned Coady in the box but then tripped over the ball.
The home crowd were becoming increasingly frustrated until, out of nowhere, Wolves got themselves back in the game. A Rayan Ait-Nouri corner was attacked by Dendoncker and his header crashed into the top corner.
With the supporters back behind them the hosts had their tails up and had a half chance through Silva, but they failed to get the equaliser before half-time and entered the break losing 2-1.
Traore was introduced, replacing Silva, as Wolves emerged for the second half looking to get back into the game.
Early on Wolves were screaming for a penalty when Ki-Jana Hoever raced into the box and crossed for Hwang. The South Korean blazed over from a few yards but was clattered by Cristian Romero, to the anger of the Wolves players and staff.
The hosts dominated the early stages and looked threatening going forward, but were almost undone by a Ruddy mistake. Ndombele tried his luck from distance and Ruddy let the ball slip straight through his hands and it flew just over the bar.
But, just before the 60th minute, Wolves got their equaliser. Hwang did brilliantly to snatch the ball and feed Dendoncker who then played in Podence. The forward slipped the ball into the bottom corner in front of a delighted South Bank.
At the other end, Ruddy made a superb save with his legs to deny Bryan Gil, before making an instinctive stop to deny Kane.
Wolves probed for a winner but eventually the game came down to a penalty shoot-out.
Kane, Sergio Reguilon and Gil scored for Spurs, while Pierre-Emile Hojbjerg had an effort saved. But for Wolves only Hwang and Joao Moutinho scored, as Neves, Dendoncker and Coady missed - condemning Wolves to a 3-2 penalty shoot-out defeat.
Wolves: Ruddy, Kilman, Boly, Mosquera (Coady, 9), Hoever, Neves, Dendoncker, Ait-Nouri (Semedo, 75), Podence (Moutinho, 84), Hwang, Silva (Traore, 45).
Subs not used: Moulden, Trincao, Jimenez.
Spurs: Gollini, Tanganga (Reguilon, 95), Romero, Sanchez, Davies, Skipp, Ndombele, Alli (Hojbjerg, 82), Gil, Lo Celso (Son, 62), Kane.
Subs not used: Austin, Doherty, Rodon, Scarlett.