Andriy Yarmolenko climbed off the bench to sink Sevilla as West Ham prolonged their European adventure with a dramatic extra-time win.
The Hammers, debutants in the knockout stage of the Europa League, stunned one of the tournament favourites and six-time winners at a raucous London Stadium.
Trailing 1-0 from the first leg, Tomas Soucek headed West Ham level in the first half.
And on a genuine European glory night for the club, Yarmolenko guided the Hammers to a 2-1 aggregate victory and into a historic quarter-final.
West Ham, who looked comfortable at this level throughout the group stage, went straight on the offensive and Pablo Fornals saw an early volley blocked.
Sevilla threatened when Manchester United loanee Anthony Martial's effort was blocked and Jesus Navas hooked the loose ball onto the roof of the net.
The Spanish side should have taken the lead in the 26th minute but Youssef En-Nesyri was denied by a superb point-blank save from Hammers keeper Alphonse Areola.
West Ham came agonisingly close moments later when Said Benrahma fed Michail Antonio in the area.
The striker, who passed a late fitness test after going off injured against Aston Villa on Sunday, saw his shot deflected by Jules Kounde and pushed out by keeper Yassine Bounou.
Soucek slid in to bury the rebound but he was just beaten to the ball by defender Nemanja Gudelj, who touched it clear.
But the Czech midfielder did strike six minutes before half-time to level the tie with a towering header at the far post from Antonio's cross.
Soucek almost had another after the break following a jinking run from Declan Rice, but Bounou saved his drive and Rice shanked the rebound wide.
West Ham had built up a head of steam and Manuel Lanzini's shot was parried with Gudelj hooking away the Argentinian's attempt to steer in the rebound.
It was at times relentless pressure from the hosts, but they had a let-off when Sevilla countered and Tecatito Corona fired over.
A late West Ham rally failed to produce a winner inside 90 minutes - Benrahma going closest with a curler held by Bounou - and the tie went into extra time.
Soucek was inches away again when he met Craig Dawson's knockdown at the far post but could not guide it home.
But Yarmolenko won it for David Moyes' men when Bounou pushed away a Fornals shot straight to him to finish at the far post, sparking joyous celebrations on the pitch and bedlam in the stands.