Gylfi Sigurdsson put the hosts ahead with an early contender for goal of the season, but the game went in to extra-time following a horrible gaffe from Brad Friedel.
Ireland international Paul McShane put Hull on course for victory in extra-time, but Harry Kane made it 2-2 before Friedel saved Ahmed Elmohamady’s penalty in a marathon shoot-out to set Spurs up with aquarter-final clash against West Ham.
Andre Villas-Boas took the controversial step of criticising his own fans after Tottenham laboured to a 1-0 win over the Tigers on Sunday, but the home faithful were in good voice last night.
The good feeling inside White Hart Lane was generated by a strong first-half performance from Villas-Boas’ side.
The home side passed with purpose and verve while Sigurdsson’s golden strike was a joy to behold.
But it was the same story in the final third for the Londoners. Only Erik Lamela looked capable of slicing open the Hull back four and Spurs only looked more potent when Kane came off the bench to join Jermain Defoe in a two-pronged attack.
Hull, for their part, looked impressive going forward, but they could not produce the goods in an absorbing shoot-out.
McLean gave Tottenham the advantage when he missed Hull’s first penalty in the shoot out, but Lamela’s miss levelled things up.
Friedel then atoned for his error by saving well from Elmohamady with his feet to send Spurs through.
SPURS: Friedel, Walker, Kaboul, Vertonghen, Naughton (Chiriches 68), Dembele, Paulinho, Lamela, Eriksen (Chadli 68, Kane 78), Sigurdsson, Defoe.
HULL: Jakupovic, Davies, Bruce (Proschwitz 34), McShane, Elmohamady, Meyler, Koren (Gedo 82), Quinn, Rosenior, Boyd, Graham (Mclean 46).
Referee: Jon Moss (W Yorkshire).