Kai Havertz's late winner in Lisbon proved decisive. Arsenal narrowly managed a 0–0 draw at home with Sporting and progressed 1–0 on aggregate.
Viktor Gyökeres had his chances. The first shot went well over and the next time the international striker had the chance to give Arsenal the lead, Gonçalo Inácio thwarted him at the last moment.
Instead, Sporting's Geny Catamo came close to equalising the match, but he hit the post.
Gyökeres played only 56 minutes before being replaced by Havertz, who didn't do much.
Substitute Leandro Trossard headed against the post late on. With the attack not firing as it had earlier in the season, the team's collective defensive play took the club to the semi-finals for the second year in a row.
Goal celebration in Munich
It was even more dramatic in the other second-leg quarter-final of the evening. Bayern Munich had a 2-1 lead at the Santiago Bernabéu to fall back on. That lead was wiped out after just 35 seconds.
Veteran goalkeeper Manuel Neuer, a giant in the first leg, made a huge blunder. A mis-kick went to Arda Güler and it was 2-2 on aggregate.
But Real were not deterred by that gift. Five minutes later, Aleksandar Pavlović headed in Joshua Kimmich's corner.
Güler wasn't finished for the evening. When he converted the free kick, he ensured the tie would go to extra time at the Allianz Arena.
Bayern turned things around at the end
Then the big stars stepped into the action. Harry Kane equalised, then Kylian Mbappé made it 2-3 - the fifth goal of the first half.
Real's Eduardo Camavinga received his second yellow card at the end of the goalless second half.
And with a minute left, Luis Diaz equalised. Michael Olise then made it 4–3 - and Bayern advanced 6–4 on aggregate.
The semi-finals:
April 28/29: Paris SG - Bayern Munich, Atlético Madrid - Arsenal.
May 5/6: Bayern Munich - Paris SG, Arsenal - Atlético Madrid.
The final will be played on May 30 at the Puskás Aréna in Budapest.
