Tottenham have saved their best form for European competition this season but the Spanish side showed all their experience to book their place in the last four of the competition.
Sevilla had an advantage coming into the game leading 2-1 from the first leg, but put themselves in pole position when they stunned the home supporters and raced into a two-goal lead inside the opening eight minutes.
Steed Malbranque scored an own goal before Freddie Kanoute silenced the home crowd with a second.
Although Jermain Defoe and Aaron Lennon levelled the scores in the second half, it came too little too late for the north London side and they crashed out of the competition 4-3 on aggregate.
Tottenham welcomed back influential club skipper Ledley King who had missed the last four months with a foot injury.
But even though the England defender was back at the heart of the defence, he could do nothing to prevent Sevilla storming into a two-goal lead.
The first strike came after just three minutes when Jose Luis Marti's corner picked out Christian Poulsen inside the box.
Poulsen's goal-bound header should have been cleared but Malbranque somehow managed to slice the ball into his own net.
Things went from bad to worse for the home side when Kanoute added a second on eight minutes.
The former Tottenham striker played a neat one-two with Aleksandr Kerzhakov before taking the ball around Paul Robinson and sliding the ball into an empty net.
The White Hart Lane faithful could not believe what they were witnessing and Tottenham needed to score four goals if they were to win the tie.
Martin Jol's side refused to lie down though and Robbie Keane should have pulled his side back into the game on 13 minutes.
The Republic of Ireland international striker broke free of the Sevilla defence, but chipped the ball straight into the path of keeper David Cobeno.
The home side came close again on 41 minutes when Didier Zokora made a bursting run into the Sevilla half and the ball fell to Dimitar Berbatov. The Bulgarian striker fired a fierce shot which flew inches past the post.
Berbatov came even closer to getting his name on the scoresheet on the stroke of half-time when his low drive cannoned back off the post.
Jol tried everything he could to help his side get back into the game and made an attacking substitution on 65 minutes when he introduced Defoe for Zokora.
And the move paid off straightaway as Defoe scored with his very first touch of the game. Jermaine Jenas' free-kick was headed away by Kanoute, Keane picked up the loose ball and drilled a shot towards goal which was turned in by Defoe.
The Spurs team seemed to have a new lease of life and Lennon snatched an equaliser just 90 seconds later.
Berbatov's cross came back off Keane and Lennon was in the right place to flick the ball past the Sevilla keeper.
Michael Dawson had a golden chance to put Tottenham into the lead on 81 minutes when Pascal Chimbonda's header picked out the Spurs defender unmarked in the box, but he fired his shot over the bar and Berbatov also went close late on in the game.
Tottenham midfielder Teemu Tainio was shown the red card in stoppage time for a rash challenge on Antonio Puerta.
Sevilla held on and kept alive their chances of winning the trophy for the second consecutive season.