Nuno Espirito Santo's side, after seeing Raul Jimenez surprisingly miss an early penalty, were second best in Germany and, in the end, downed by the Argentinian in the 88th minute.
Five-time competition winners Sevilla now go on to face Manchester United in the semi-finals on Sunday, while Wolves' 2019/20 has reached its belated conclusion.
A disappointing night in Duisburg but, on the whole, a remarkable ride across the continent.
It was all going so well when Adama Traore, with a trademark run, won Wolves an early penalty.
But after Jimenez saw his spot-kick saved, this tense tie only looked like ending one way at the MSV Arena.
Having started out in the competition all the way back on July 25 of last year, taking in a hugely-demanding Premier League campaign along the way too, this was just simply one match too far for Wolves.
Jimenez's miss saw Wolves' spirits take a significant dent, and come the final whistle they were absolutely shattered.
Sevilla deservedly go through while Nuno's lot look to dust themselves down and refresh in the short time they have before the league starts again.
This season is now over and, on the whole, it has been such a great trip. It was not their night, but there is still an enormous amount to be proud of.
Wolves made two changes to the side which squeezed past Olympiacos in the last 16 at Molineux.
Both of them were enforced, with Ruben Vinagre coming in for Jonny Castro Otto – the Spaniard set for up to nine months out with an anterior cruciate ligament injury.
The other saw Leander Dendoncker replace the suspended Daniel Podence as Nuno opted for a 3-5-2 formation, with Traore partnering Jimenez in attack. Wolves also had 11 substitutes instead of the permitted 12 because of Podence's ban.
Sevilla, meanwhile, stuck with the same XI which beat Roma 2-0 at this stadium last week.
The plan seemed to be to stay compact, especially with Dendoncker bulking out the midfield, and look to find joy with the sheer pace of Traore on the counter – even though playing him as a central striker has had mixed results in the past.
And it almost brought Wolves an early lead. Traore, right from the get-go, looked like hurting Sevilla every time he had the ball at his feet.
A cross to Jimenez, who headed straight at Bono, was a warning sign before the frighteningly-fast forward put on the afterburners to devastating effect.
His stunning, gut-busting 50-yard dash left a trail of white shirts in his wake and Diego Carlos, with a desperate lunge, then cynically took Traore down for a stonewall penalty and definite yellow card.
But what followed was scarcely believable.
Jimenez, having been so exceptional from the spot in his time in gold and black, saw his effort saved by Bono – although he had begun to encroach off his line.
The Moroccan read Jimenez like a book and clawed away his side-footed shot, which, admittedly, was also at a nice height for the keeper.
That was Jimenez's first competitive penalty miss for Wolves.
It knocked the stuffing out of them for the rest of the half, too. From that point, until the relief of the referee's whistle signalling the interval, it was all Sevilla.
Wing-backs Matt Doherty and Vinagre barely mustered an attack between them as the Spanish side dominated possession.
Youssef En-Nesyri dragged a strike wide with his right foot, Suso had a rasper blocked by Romain Saiss and Joan Jordan tested Rui Patricio from long range.
None of it was clear-cut, but it was enough to make you feel very anxious. They had 71 per cent possession in the first half.
Wolves, apart from a speculative Joao Moutinho volley and Jules Kounde denying Jimenez with a fine recovery tackle, had failed to unsettle Sevilla post-penalty and needed to lift it for the second period – something they have done plenty of times in the past.
A Saiss booking arrived upon the restart, while Sevilla continued to threaten.
Nuno's charges began to creep up the pitch, but it was not sticking up top.
Jimenez had a couple of loose touches and overhit some passes, and Traore – not a natural when it comes to holding the ball up – often found himself crowded out.
The Spanish outfit were creating more meaningful opportunities, as well.
Jordan's toe-poked attempt deflected out for a corner, and En-Nesyri then nudged one into the gloves of Patricio.
Not long after that, Kounde spurned a glorious opportunity as he headed over from close range.
A massive let-off for Wolves, who swiftly switched to 3-4-3 as Pedro Neto replaced Moutinho.
Jota came on for Traore, too.
But the backs-to-the-wall trend carried on until Sevilla, finally, made a breakthrough.
An Ocampos flick-in flew past the despairing Patricio and into the far corner, bringing an amazing European adventure to an end.
Wolves (3-5-2): Patricio; Boly, Coady (c), Saiss; Doherty, Neves, Dendoncker, Moutinho (Neto, 71), Vinagre; Traore (Jota, 79), Jimenez
Subs not used: Ruddy (gk), Sondergaard (gk), Marques, Kilman, Buur, Richards, Jordao, Gibbs-White, Campana
Sevilla (4-3-3): Bono; Navas (c), Kounde, Carlos, Reguilon; Jordan (Vazquez, 85), Fernando, Banega; Ocampos, En-Nesyri (De Jong, 85), Suso (Munir, 89)
Subs not used: Vaclik (gk), Diaz (gk), Gomez, Escudero, Torres, Mena, Lara, Genaro, Perez
Goal: Ocampos (88)
Referee: Daniele Orsato (Italy)