Bayer Leverkusen failed to break down an organized Atalanta side as they crashed out of the Europa League following a 1-0 home defeat on Thursday.
Teenage star Florian Wirtz was missing having torn his cruciate ligaments at the weekend and without his inspiration from midfield Leverkusen rarely looked like overcoming their 3-2 first leg deficit.
And a fine counter-attacking goal from Jermie Boga deep into injury-time then capped Atalanta's display by earning them victory on the night.
"We had chances, but not convincing ones," said Leverkusen's Robert Andrich. "We let their defenders eat us up.
"We must accept any criticism that we aren't scoring in crucial moments. We just weren't assertive enough. Atalanta showed us what it takes to win knockout matches."
The Italians will be joined in Friday's quarter-final draw by Barcelona, who came from behind to win 2-1 at Galatasaray and progress by the same score after a goalless home leg.
Defender Marcão headed the opener for Galatasaray but Pedri levelled before half-time with a with a lovely solo goal.
Pierre-Emerick Aubameyang then bagged the winner five minutes after the restart after keeper Iñaki Peña, who is on loan from Barcelona, made saves from Sergio Busquets and Pedri.
"We played a match of huge personality," said Barcelona coach Xavi. "It was a great performance to fight back in a ground like this against a very good team.
"They knew how to defend against us but we were patient. I'm very happy for my players."
Rangers also progressed to the last eight despite losing 2-1 to Red Star in Belgrade having won 3-0 in Glasgow while Braga's 1-1 draw at Monaco gave them a 3-1 aggregate triumph.
Eintract Frankfurt, Lyon and record winners Sevilla are defending first leg leads in the late kick-offs while RB Leipzig were given a bye to the quarters as Russian opponents Spartak Moscow were banned following the invasion of Ukraine.
