Villarreal will now play Manchester United in the May 26 final in Gdansk in what will be the biggest night in their history.
Villarreal held out for a 0-0 draw on a nerve-jangling night at Arsenal on Thursday to reach the Europa League final 2-1 on aggregate as visiting manager Unai Emery returned to haunt the London club that sacked him in 2019.
The Spanish side, who had lost their four previous European semi-finals, one to Arsenal in the 2005-06 Champions League, protected their first-leg advantage with a disciplined display.
They will now play Manchester United in the May 26 final in Gdansk in what will be the biggest night in their history.
Arsenal, who now face the prospect of having no European football next season for the first time in 25 years, looked flat and never managed to exert any sustained pressure.
"We are devastated, really disappointed," said Arsenal boss Mikel Arteta, who was dealt a blow in the warm-up when Swiss midfielder Granit Xhaka was injured and had to be replaced by full back Kieran Tierney.
Unai Emery has coached in the Europa League nine different seasons. He's made the final in five of them 😱— B/R Football (@brfootball) May 6, 2021
2014 (Sevilla): 🏆
2015 (Sevilla): 🏆
2016 (Sevilla): 🏆
2019 (Arsenal): 🚫
2021 (Villarreal): ⏳ pic.twitter.com/cieehXM8ab
"But we congratulate Villarreal. I think we deserved to win the game but the details define these ties. The way we started in Villarreal wasn't good enough."
It was a desperately disappointing night for Arsenal that begun with a large group of fans again demonstrating against the club's American owner Stan Kroenke and ended with Spaniard Arteta facing increasing pressure over his future with Arsenal languishing in ninth spot in the Premier League.
His misery contrasted sharply with the mood of Emery who now takes the so-called Yellow Submarine to Poland on May 26 with the chance to win his fourth Europa League having done so three times in a golden period with Sevilla.
"I'm very proud, Arsenal are a very good team but I think we deserved it," he said. "We made a very serious match, we all helped each other, we defended very well and sometimes with the possession we controlled the match."
Looking ahead to the final he said: "It will be very difficult but we deserve to play this final and we will show our supporters our best performance again."
Emery's canny Villarreal side were worthy winners over the two legs although they rode their luck on a couple of occasions at The Emirates on Thursday when Arsenal skipper Pierre-Emerick Aubameyang twice hit the post.
The Gabon striker thumped a volley against the upright in the 25th minute, although that was a rare Arsenal chance in a first half in which they showed an alarming lack of intensity considering the prize on offer.
Aubameyang then went even closer after the break when his header from Hector Bellerin's cross hit the inside of the post and somehow did not spin across the line.
Emile Smith Rowe also lobbed the ball narrowly wide for the Gunners while Rob Holding saw a header flash past the post.
But the Spanish visitors were calm and composed in possession and might have put the tie to bed had Gerard Moreno made more of a glorious chance early in the second half instead of shooting straight at Arsenal goalkeeper Bernd Leno.
Villarreal's players celebrated loudly at the final whistle after surviving five minutes of stoppage time.
2019: Sacked by Arsenal— ESPN FC (@ESPNFC) May 6, 2021
Today: Knocks Arsenal out of the UEL
A very good ebening for Unai Emery 😏 pic.twitter.com/zcrJOR0BDM
"Tonight I'm crying tears of emotion instead of disappointment," said Villarreal youth product Pau Torres, now 24, who admitted crying when he watched the 2006 Champions League semi-final defeat by Arsenal.
"Villarreal have missed out on so many semi-final chances to reach the final but now, finally, we've done it."