Lucas Ocampos glanced in with two minutes remaining to send the Spanish side into the semi-finals.
Sevilla moved a step closer to a sixth UEFA Europa League/UEFA Cup title after a late Lucas Ocampos header saw off Wolves.
Wolves made the quicker start and were rewarded when Adama Traoré's marauding run was halted by Diego Carlos in the area. However, Raúl Jiménez, usually so reliable from the penalty spot, was denied by Yassine Bounou. Sevilla had the greater possession thereafter but Suso's long-range drive, that was parried by Rui Patrício, was as close as they came in the first half.
Julen Lopetegui's men were back on the front foot after the break with Jules Koundé heading over Suso's teasing cross and Rui Patrício tipping over Éver Banega's free-kick. Wolves eventually buckled, though, as Banega's late set piece was expertly guided in by Ocampos to book a semi-final against Manchester United on Sunday.
Tom Kell, Wolves reporter
After a season spanning 59 games – 17 of them in this competition – and well over 12 months, is it any surprise that Wolves eventually ran out of steam? They looked to win this match early on and should have taken the lead their electric start deserved, but for the final hour they were second best and visibly fatigued. "Dreaming is for free" said Nuno Espírito Santo back in February – it's been quite the adventure for Wolves fans but, at last, now it's over.
Joe Walker, Sevilla reporter
What is it with Sevilla and this competition? They just know how to get the job done and, despite not being at their best, they have sealed their place in the last four. Now you would not back against them securing a sixth UEFA Cup/UEFA Europa League title. It wasn't pretty, but Lopetegui won't care one jot.
Yassine Bounou, Sevilla goalkeeper: "It's a relief. We came up against a good side who are really tight at the back. They were well set up and it was so tough to cause them any sort of harm, so when the goal arrived we felt that kind of relief just spill out of us."
Nuno Espírito Santo, Wolves manager: "The last minute [goal] is something that's happened to us too many times, but I'm proud of the boys. We played a tough team but it's all about small margins. We came this far, now it's over – let's rest and look to the future."
- Sevilla are unbeaten in 19 matches (W10 D9) – this includes winning seven of their last eight games.
- Sevilla have not conceded a goal in their last five matches.
- Sevilla's victory was their 40th in the UEFA Europa League – a new record
- Sevilla have not conceded a first-half goal in their ten UEFA Europa League games this season.
- Raúl Jiménez had scored all eight of his penalties for Wolves before tonight.
Wolves: Rui Patrício; Boly, Coady, Saïss; Doherty, Dendoncker, Moutinho (Neto 71), Neves, Vinagre; Traoré (Jota 79), Jiménez
Sevilla: Bounou; Navas, Diego Carlos, Koundé, Reguilón; Banega, Fernando, Jordán (Vázquez 84); Suso (Munir 89), En-Nesyri (De Jong 85), Ocampos
Sevilla will face Manchester United in the semi-finals on Sunday in Cologne, with the final at the same venue five days later.