Where to start?
The basics are that after we took the first leg 3-0 at the Lane, Inter levelled the aggregate scoreline with goals from Antonio Cassano in the 20th minute, Rodrigo Palacio in the 52nd minute and then a William Gallas own goal in the 75th minute.
That took the tie into extra time where finally we grabbed the away goal we craved - and ultimately proved crucial - as Adebayor slid in the rebound after Samir Handanovic palmed out Gylfi Sigurdsson's drive.
Inter wouldn't lie down though and scored again when Ricardo Alvarez headed home from close range in the 110th minute.
They still needed another goal to take the tie 5-4 - thankfully Andrea Ranocchia missed the target when the final chance arrived.
Players from both teams collapsed to their knees when referee Ivan Bebek blew the final whistle - it had been an epic encounter.
Andre Villas-Boas made four changes to the team that started at Anfield on Sunday.
Adebayor partnered Jermain Defoe up front after returning from injury and defensively, Brad Friedel was back for Hugo Lloris, Gallas replaced Michael Dawson and captained the team while Kyle Naughton started at left-back for Benoit Assou-Ekotto. Aaron Lennon also returned on the bench.
Inter got behind us a couple of times before taking the lead. Cassano drove straight at Friedel from a tight angle on 13 minutes and then looked for penalty before heading home the opener from Palacio's on 20 minutes.
Sigurdsson tested Handanovic with a curler from 22 yards but Inter soon broke clear again, Palacio this time raced onto Cassano's pass and lobbed over Friedel, only to see his effort clip the top of the crossbar.
Defoe zipped past Cristian Chivu but crossed behind Adebayor and Kyle Walker rose well to meet Sigurdsson's free-kick on 37 minutes, but glanced wide.
The final chances of the half arrived in injury time. Fredy Guarin drifted inside Walker from the left and blasted at Friedel, who did well to palm away and seconds later Adebayor was clear on the edge of the box and looked to lift over Handanovic, his effort clearing the crossbar.
We started the second half brightly and Adebayor almost carved a chance out for Jan Vertonghen on 51 minutes. He burst away from Jonathan and cut back to Vertonghen in support, but Chivu did enough to block.
Less than a minute later though and Inter pulled another goal back. Esteban Cambiasso rolled the ball into Palacio on the left side of the box and he made no mistake, sliding across Friedel and home.
Twenty minutes later and the stadium went crazy as Inter levelled the aggregate scoreline.
Cassano aimed to curl a free-kick at goal from the left edge of the box, it flicked off the defensive wall and Gallas turned the ball into his own net.
Naughton came close to finding the now-vital away goal five minutes from time when he let rip from 25 yards only to see Handanovic turn away to his left.
Inter had the chance to clinch it at 4-0 in the final seconds as Cambiasso went clear in the left channel of the box, but he dragged his shot inches wide of the far post.
We started with real intent in extra time. Lennon, off the bench in the 69th minute, had a sight of goal in the second minute only to find Zanetti in his way when he pulled the trigger.
Vertonghen climbed high to meet Sigurdsson's corner only for Handanovic to somehow palm the ball past the post from his goalline. That meant another corner, and this time Gallas met it 10 yards out - but missed the target.
The breakthrough arrived in the 96th minute. Sigurdsson was involved again, cutting onto his right foot and letting fly from 22 yards. Handanovic did well to parry but Adebayor was there, sliding between Zanetti and Chivo to prod into the empty net.
That meant Inter had to score twice to go through and initially, you felt the home fans thought that was that.
But their team lifted themselves again. Palacio forced a sharp save from Friedel at the start of the first half of extra time and the goalkeeper was there again to tip away Cassano's curler in the 106th minute.
Inter pulled level on aggregate with their fourth goal on the night as substitute Alvarez powered home his header at the far post from Cassano's cross in the 110th minute.
We coped well as Inter desperately searched for what would have been a winner and it wasn't until the 120th minute that the final chance arrived. Handanovic came up for a corner that Cassano actually took short before curling to the far post where Ranocchia climbed well but couldn't keep his header on target.
Spurs (4-4-2): Friedel; Walker, Gallas, Vertonghen, Naughton (Caulker, 104); Dembele, Livermore (Lennon, 69), Parker, Sigurdsson; Adebayor, Defoe (Holtby, 56). Unused subs: Lloris, Assou-Ekotto, Carroll, Huddlestone.
Inter Milan (4-4-2): Handanovic; Jonathan (Ranocchia, 107), Chivu, Juan, Zanetti; Gargano, Kovacic (Benassi, 79) , Guarin (Alvarez, 71), Cambiasso; Cassano, Palacio. Unused subs: Belec, Pasa, Colombi, Belloni.
Yellow cards: Inter - Juan. Spurs - Livermore, Friedel, Holtby, Adebayor.
Goals: Inter - Cassano (20), Palacio (52), Gallas (own goal, 75), Alvarez (110). Spurs - Adebayor (96).
Referee: Mr I Bebek (Croatia).
Attendance: To follow...
Inter clawed their way back into the tie at 3-0 and had chances to knock us out in injury time and then in the final minute of extra time at 4-1, but thankfully we held on and Emmanuel Adebayor's goal in the 96th minute - the only away goal of the tie - proved decisive.