Trailing 3-0 from the first leg, Inter, playing with belief throughout, stormed back into the tie with goals from Antonio Cassano and Rodrigo Palacio before an own goal from William Gallas leveled the tie up on aggregate.
The home side had the opportunity to claim the win in the dying seconds but Esteban Cambiasso fired wide and Tottenham composed themselves in extra time and struck the crucial goal early on to leave Inter needing to score twice to progress. They pulled one of those back through Ricky Alvarez, but just came up short of a most remarkable turnaround.
Inter were a transformed team from the match a week ago at White Hart Lane and deserve plenty of credit, but questions will also be asked about an incredibly sloppy Spurs performance that was summed up by a dreadful display from Gallas.
In front of a sparse crowd at the San Siro, there appeared little hope of an Inter side beset by injuries and poor form producing an improbable victory, but time and again the home side troubled Tottenham’s rearguard.
Spurs’ high defensive line was caught out repeatedly in the early stages by simple balls over the top. Twice Cassano broke free through that strategy in the opening minutes. On the first occasion his shot from the right of the box was saved low by Brad Friedel, but an almost replica scenario shortly after led to vociferous appeals for a penalty as Cassano went down under a challenge from behind by Gallas. There was definitely contact, although it is debatable whether it was enough to warrant a spot kick.
Inter’s attacking threat was to be rewarded on 20 minutes. In the blink of an eye Jonathan slid in Palacio down the right and the forward supplied an instant pinpoint cross to the back post where Cassano was on hand to produce a textbook header into the ground and past Friedel.
While Gallas’s slowness of feet and mind wasn’t helping, Tottenham were also more vulnerable due to the presence of Friedel in place of Hugo Lloris. The veteran American remains a fine keeper between the sticks, but Lloris’s covering ability, becoming an almost sweeper, has been a big part of Spurs’ success this season.
The visitors problems at the back were exposed again when Cassano played a wonderful ball over the top and Palacio raced onto it. With Friedel out to the edge of the box, the Argentinian rightly tried the lob but the ball came back off the crossbar.
In the final seconds of the first half both sides had chances to score goals that would have altered the complexion of the tie dramatically. Cassano again hit a ball over the top, this time to Fredy Guarin, who was forced wide but cut inside before firing a shot that Friedel had to be alert to beat away.
Seconds later, Spurs had the opportunity to leave Inter needing four more goals when Juan failed to win the ball decisively from Jermain Defoe and the ball ran to Adebayor but he chipped his effort over the bar.
Within seven minutes after the restart, though, Inter had put the tie firmly in the balance and again it was Gallas who was caught out. Cambiasso won the ball in the middle of the pitch and moved forward before slipping in Palacio, who easily peeled away from Gallas before sliding the ball low past Friedel.
Spurs boss Andre Villas-Boas soon looked to respond by brining off Defoe for Lewis Holby, presumably with the aim of providing more security in midfield.
It was still Inter that were controlling proceedings, however, and with 15 minutes remaining Gallas furthered his own personal nightmare of a performance. Cassano whipped in a poor free-kick that deflected off the wall for what should have been a simple clearance at the back post for Gallas, but the 35-year-old took a wild lash at the ball and slashed it into his own net.
In the final dramatic minutes of regulation time both sides came close to grabbing a winner. Samir Handanovic produced a stunning save at full stretch to deny Kyle Naughton’s powerful effort from outside the box.
And with seconds remaining Gallas gifted Inter yet another opportunity, this time to Cambiasso, but the Argentinian poorly dragged his shot wide inches wide.
The goalmouth action continued immediately in extra time as Vertonghen had a header saved by Handanovic, before Gallas continued his miserable night by heading wide from six yards out with a clear sight of goal.
Spurs had started to play with more intent than at any other point in the match and they stunned Inter six minutes into extra time. Mousa Dembele strode forward and fired a powerful low shot from 20 yards that Handanovic could only parry out in front of him and Adebayor was on hand to stretch and steer the ball into the net for his first meaningful contribution of the evening.
But Inter were not quite done. With 10 minutes left of extra time, substitute Alvarez snuck in at the back post and headed home from Cassano’s excellent cross.
Incredibly Inter carved out yet another chance to win the tie in the final minute but Andrea Ranochhia headed over the bar as Tottenham clung on to progress in the most unconvincing of fashions.