Bayern Munich were sent crashing out of the Champions League as Samuel Chukwueze's 88th-minute strike secured a dramatic 2-1 aggregate victory for underdogs Villarreal
Substitute Chukwueze, who had only been on the pitch for four minutes, finished off a rapid counter-attack when he converted Gerard Moreno's cross to silence the Allianz Arena as Bayern were eliminated at the quarter-final stage for the second year in a row
Bayern had been pushing for a winner of their own after Robert Lewandowski cancelled out Arnaut Danjuma's first-leg strike with his 13th Champions League goal of the campaign early in the second half
But Unai Emery's side, Europa League winners against Manchester United last season, defended resolutely in the face of heavy Bayern pressure and seized their chance when it came
Indeed, while Bayern had 45 shots across the two legs and only scored once, Villarreal netted with each of their only two efforts on target, with Chukwueze's breakaway strike meaning they will face either Liverpool or Benfica in only the second Champions League semi-final in their history
Villarreal had been deserving victors in the first leg, a game they were unfortunate not to win by a bigger margin, and while Bayern boss Julian Nagelsmann promised there would be no repeat of his side's lacklustre showing back in Germany, the first half brought more of the same
Bayern, nine points clear at the top of the Bundesliga, struggled to break down the side sitting seventh in La Liga, resorting to a succession of crosses which were, for the most part, easily dealt with by centre-backs Raul Albiol and Pau Torres
Jamal Masiala did manage to connect with one centre from Leon Goretzka just before the half-hour mark, but the youngster sent his header straight at Villarreal goalkeeper Geronimo Rulli
It would prove Bayern's only shot on target of the first period and, while Villarreal spent most of the half camped inside their own half, they looked more incisive than Bayern when springing forward
Moreno fired wide with two powerful shots, one of which went into the side netting, while Danjuma mis-hit when one on one with Manuel Neuer, although replays showed he may have been offside from Etienne Capoue's through-ball
Bayern finally showed signs of life after the break and their increased intensity brought a goal when Villarreal lost possession near the halfway line, allowing Thomas Muller to feed Lewandowski, whose early shot from the edge of the box bounced in off the post
The Allianz Arena erupted in celebration and it seemed only a matter of time until Bayern edged in front in the tie
Muller was guilty of spurning their best chances, firing high and wide under pressure from Giovani Lo Celso on one occasion, then sending a free header past the post from a Leroy Sane cross
But Villarreal weathered the storm and the winning goal exemplified their composure and efficiency in testing circumstances
Raul Albiol's defensive header fell to Dani Parejo, who kept his cool on the edge of his own box to find the onrushing Lo Celso, who in turn slid the ball through to Moreno
The striker was onside from the Spurs loanee's pass, and immediately squared the ball for Chukwueze, who lifted his finish over Neuer to spark delirium among the travelling supporters as Bayern's players and fans looked on in disbelief
Bayern boss  said: "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 semi-finals as our minimum goal and we failed to achieve it
 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
"Arsenal fans may not have the fondest memories of Unai Emery but Villarreal's latest European giant-killing serves as a reminder of his extraordinary pedigree in continental competition
Emery, who guided serial overachievers Villarreal to Europa League glory against Manchester United last season, has now steered the club to only its second-ever Champions League semi-final
Villarreal's Europa League triumph last May was the fourth of Emery's managerial career and the 50-year-old deserves acclaim for transferring that success to the Champions League this season
Villarreal pulled off a stunning 3-0 win away to Juventus to secure their spot in the last eight but their elimination of Bayern, a side sat nine points clear at the top of the Bundesliga, was even better
Emery outmanoeuvred Julian Nagelsmann in the first leg and Tuesday's second-leg performance, in the cauldron of the Allianz Arena, where Bayern had smashed 20 goals in their previous six games in all competitions, was even more impressive
They defended impeccably, shutting off the spaces Bayern like to operate in and instead forcing them to resort to a succession of hopeful crosses from wide areas
 Then, when they had chances to spring forward, they did so with confidence and conviction
The word masterclass is bandied around too readily in modern football but Emery's managerial performance over the two legs, against one of Europe's strongest sides, must go down as one
Bayern dominated possession and territory across the 180 minutes but Villarreal controlled and contained them in Spain and, save for a period of around 20 minutes after half-time on Tuesday night, they did the same in Germany
Jurgen Klopp's Liverpool are likely to be next but they will hold no fear for Villarreal - not when they have European specialist Emery guiding the way
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