Champions League debutants Villarreal claimed their place among Europe's soccer elite after weathering a late storm from Everton to win 2-1 on Wednesday.
The Spaniards, who also won 2-1 in the first leg at Goodison Park, looked on course for a comfortable victory when Argentine midfielder Juan Pablo Sorin put them ahead with a deflected shot after 20 minutes.
But a sweetly struck free kick from Spanish midfielder Mikel Arteta 20 minutes from time brought the game to life and gave David Moyes' side renewed hope of staging a comeback.
Everton striker Duncan Ferguson fired home a bullet header nine minutes from time only to see his goal disallowed by referee Pierluigi Collina and Villarreal were on the ropes for the remainder of the match.
But former Manchester United striker Diego Forlan settled the tie a minute into injury time when he added the finishing touch to a devastating counter attack when he poked the ball past Martyn.
For Everton the 4-2 aggregate defeat brought a rapid end to their first European Cup campaign in 34 years, while Villarreal will now join Barcelona, Real Madrid and Real Betis as part of a quartet of Spanish sides in the last 32.
"We have achieved our first objective with qualification, but this is not the end of our ambitions," said Villarreal coach Manuel Pellegrini.
"Everyone said Everton were a tough side to beat, but I was always optimistic we could make it through amd the team proved me right."
SLICK PASSING
Villarreal began the match by trying to draw the sting out of the Everton attack, forcing them to chase the ball with some slick one-touch passing in midfield and they took the lead after a slick break started and finished by Sorin.
The midfielder exchanged a sharp one-two with Juan Roman Riquelme before unleashing a shot from the edge of the area that took a deflection off defender David Weir before swerving past Nigel Martyn into the net.
Martyn produced a string of saves either side of the break to keep Everton in the match but the Premier League side were thrown a lifeline in the 70th minute when Arteta curled his perfectly struck free kick around the wall and inside the post.
The visitors looked to have taken the lead 10 minutes from time when Ferguson powered home a header from a corner only to see his goal harshly disallowed after Marcus Bent was adjudged to have fouled a defender.
Everton surged forward into attack for the remainder of the match, but were finally put to the sword when Forlan side-footed home past Martyn after Riquelme and Sorin had combined to slice open the opposition defence.
"We missed some chances and everything changed when they scored that goal but we knew it was going to be tough," Forlan told ITV 2.
"In the second half it was difficult, that disallowed goal was helpful for us."
Everton manager David Moyes was pleased with the spirit shown by his players in the club's first European tie for 10 years but annoyed at Collina's decision. "Maybe it's new to us and we need to understand more," he said.
"I was told referees would be the same in Europe as they are in England.
"We are disappointed we are out but must not forget the achievement of getting here - so now we get a chance in the UEFA Cup."