The hosts go through after a shootout that followed 120 minutes of highly uninspiring football, after both managers made significant changes to their teams for third round clash
Both sides made several changes from their weekend games and both managers had suggested that the tie was an unwelcome addition to their Premier League and Europa League commitments.
Neither team were able to take the upper hand in the early stages, and Wilson Palacios was warned by referee Lee Probert after clattering former team-mate Rafael van der Vaart in the opening minutes of the match.
Stoke were dealt an early blow when Kenwyne Jones picked up a suspected hamstring injury and had to be replaced by Peter Crouch, who recieved a warm reception from both sets of supporters, lining up against his former team.
The home side had the first half-chance of the match as Huth headed over from Matthew Etherington's corner.
The Potters had settled into a pattern of playing long balls up to Crouch but he was dealt with comfortably throughout by Spurs' central defensive partnership of Sebastien Bassong and Younes Kaboul.
However, Crouch was involved in another Potters chance just after the half hour when a deep cross found the England forward at the back post. His header across the area would have given Cameron Jerome an easy chance but Kaboul was on hand to intercept and clear the ball away.
Brazilian midfielder Sandro, making his comeback from injury, did not show any ill effects as he fizzed a shot towards the Stoke goal but Sorensen saved comfortably.
Stalemate | Both sides cancelled each other out in normal time
Spurs looked to end the first half well and could have taken the lead when Roman Pavlyuchenko's cross found the on-rushing Thomas Carroll, but the youngster's lack of composure saw the ball flying high over the crossbar.
The game remained goalless at the break with neither side showing a real desire to take the game.
Spurs came out for the second period showing much more attacking intent. A short corner was worked into Jake Livermore's path but his shot squirmed just past the post.
Harry Redknapp's men continued to attack and good work down the right-hand side found Pavlyuchenko in the box. With Giovani dos Santos in a good position, the Russian decided to take it on himself and forced a smart save from Sorensen.
Stoke were unable to get back into the match, and were fortunate not to go behind when Van der Vaart was fouled on the edge of the penalty area and his resulting free-kick smashed through the wall and went only narrowly wide.
The hosts finally managed to trouble Spurs keeper Heurelho Gomes when he struggled with an Etherington cross, clearing it at the second attempt, showing the kind of frailties that have seen him fall behind Brad Friedel in the pecking order.
After a bright start to the second period, the play soon deteriorated with neither side able to create any clear-cut chances as the game drifted into extra time.
Jonathan Walters had a golden chance to open the scoring for Stoke right at the end of the first period of extra time when played through one-on-one, but he dragged his effort wide of Gomes' far post.
With no further chances in the remaining time, a penalty shoot-out was required to separate the teams.
Both opening spot-kicks were scored, but Jermaine Pennant hit the cross bar for Stoke and when given the opportunity to give Spurs the advantage, Pavlyuchenko blazed his effort over to complete an abject night for the Russian.
The spot-kicks continued to go in well into sudden death, Crouch and Etherington scoring against their former clubs, while Spurs' youngsters Livermore and Carroll showed maturity in slotting home.
However, following Ryan Shotton's succesful strike for the hosts, Spurs substitute Massimo Luongo saw Sorensen save his kick to send Stoke through to the fourth round.