Emmanuel Adebayor scored in extra-time as Spurs lost 4-1 to Inter but progressed to the Europa League quarters 4-4 on away goals.
Tottenham crushed Inter 3-0 in the first leg, but the Italian giants completely outclassed Andre Villas-Boas's shellshocked side in the first 90 minutes of this game.
Spurs, without suspended star man Gareth Bale, dominated the early exchanges, but they did not test goalkeeper Samir Handanovic.
Antonio Cassano opened the scoring when he got on the end of a Rodrigo Palacio cross after Jonathan cut out Kyle Naughton and headed home from six yards.
Inter did not relent and almost added a second goal in the 26th minute when Cassano threaded a ball through Kyle Walker and William Gallas to find Palacio, but the Argentinian's lob cannoned off the crossbar and over.
Tottenham held back the tide before the interval, but soon after the restart Cassano found Palacio with a through-ball and he curled a shot beyond Brad Friedel to make it 2-0.
Inter's quest to find a third looked set for failure until they won a free-kick 25 yards out with 15 minutes to go. Cassano struck the wall with a powerful low effort but it squirmed through and Gallas stuck out a leg and poked the ball past an off-balance Friedel.
Villas-Boas gathered his team together after the referee signalled led the end of the normal 90 minutes and Tottenham seemed reinvigorated by the talk from their manager. Handanovic saved well from Aaron Lennon and Jan Vertonghen, while Gallas headed wide unmarked from eight yards.
Adebayor did not miss the target moments later, however, stabbing past Handanovic after the Inter goalkeeper spilled Mousa Dembele's shot.
The 2,000 travelling fans erupted in ecstasy, but they were back biting their finger nails again in the 110th minute when Ricardo Alvarez nodded home from Cassano's cross to make it 4-4 on aggregate. The away goal meant Tottenham remained on course to go through, and despite late attempts from the home side Villas-Boas' team held on to enter the hat for the quarter-finals.
MAN OF THE MATCH
Rodrigo Palacio (Inter Milan) - A superb effort from him and Antonio Cassano. Inter at least restored pride in defeat. A completely different effort from that 3-0 shredding at Spurs a week ago.
INTER MILAN: Handanovic 7, Jonathan 7, Juan 6, Chivu 7, Zanetti 7, Gargano 7, Kovacic 7, Cambiasso 7, Guarin 6 Palacio 8, Cassano 8; Subs: Alvarez 6, Ranocchia 6, Benassi 6.
TOTTENHAM: Friedel 6; Walker 5, Gallas 4, Vertonghen 4, Naughton 5; Dembele 5, Livermore 5, Parker 5, Sigurdsson 5; Adebayor 5, Defoe 4; Subs: Caulker 5, Holtby 5, Lennon 5.