Underdogs Villarreal scored an 88th minute equaliser through substitute Samuel Chukwueze to snatch a stunning 1-1 draw at Bayern Munich and advance to the Champions League semifinals with a 2-1 aggregate win on Tuesday.
Six-time European champions Bayern, who had won 12 of their previous 13 home games in the competition,levelled the tie when Robert Lewandowski drilled the ball in off the post after 52 minutes with his 13th Champions League goal of the season.
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But they failed to find the net again despite intense pressure in the second half and several missed chances.
Instead it was Villarreal, semifinalists in 2006, who scored against the run of play with Chukwueze beating goalkeeper Manuel Neuer with a left-foot effort to silence the home crowd.
They will play Liverpool or Benfica in the last four, with the English side leading 3-1 after the first leg in Portugal.
Bayern coach Julian Nagelsmann fielded an extremely attacking formation with Jamal Musiala, Lewandowski and Thomas Muller up front but they had only one effort on target in the first half with Musiala's weak header on the half hour mark.
After the match, Nagelsmann, whose Bayern are nine points clear of second-placed Borussia Dortmund atop the Bundesliga with five matches remaining, said a season without Champions League success was a failure.
"We are out of the German Cup, out of the Champions League. I don't think this is good enough for Bayern. We had the semifinals as our minimum goal and we failed to achieve it," Nagelsmann said. "It counts as one of my top three defeats.
"What happened is we lost the duel. With our performance today you saw the emotions and the good tactics we played. It was quite the opposite from the first leg.
"We knew they can defend. At the end we missed that second goal. The pressure was good. We defended well. We dominated them for much of the game but it matters little because we are eliminated."
Villarreal, unchanged from last week's 1-0 win, were comfortable with staying back and efficiently absorbing the waves of Bayern attacks while remaining a threat on the break.
But Unai Emery's team looked out of sorts after the break, piling up errors and losing possession as Bayern instantly upped the pressure.
Bayern defender Dayot Upamecano should have done better when his shot from eight metres flew over the bar in the 49th minute but Lewandowski did not miss three minutes later.
Bayern intercepted a sloppy Villarreal pass and the Pole finished the quick move with a low drive off the post.
The Bundesliga side, who had scored a total of 20 goals in their previous four home games in the competition this term, came close to a second goal in the 71st but Muller's diving header went wide.
It was left to Villarreal, Europa League winners last year, to punished the home side on the break through winger Chukwueze, to reach the semis for the first time in 16 years.