Extra time beckoned following Robert Lewandowski's second-half goal, but after soaking up so much pressure the Spanish side struck late to set up a semi-final against Liverpool or Benfica.
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Villarreal's remarkable UEFA Champions League campaign continues as a resilient back-to-the-wall display set the foundation for a dramatic smash and grab at Bayern München, substitute Samu Chukwueze coming off the bench to complete an electric counterattack with only two minutes remaining.
52' Clinical Lewandowski levels tie
72' Müller heads fine chance wide
84' Chukwueze comes off visitors' bench
88' Chukwueze sends Villarreal through!
Match in brief: Chukwueze snatches it at the last
The onus was on Bayern following last week's 1-0 defeat in Spain, and the home side took up the responsibility from the off, setting up camp in the Villarreal half. Yet for all their intent the Bundesliga champions reached the interval with little in the way of meaningful chances to show for it.
Much of the credit went to the visitors' yellow wall, but one lapse seven minutes into the second period and all the good work was undone as Kingsley Coman capitalised on a loose pass out of defence. The ball was recycled through Thomas Müller and then Lewandowski, who coolly applied the clinical finish.
Villarreal were rocking for a while, but 36-year-old Raúl Albiol helped them back onto their feet before Chukwueze unleashed the sucker punch. It was a move that began right on the edge of their own box, Dani Parejo and Giovani Lo Celso leading the charge before Chukwueze swept in Gerard Moreno's cross.
PlayStation® Player of the Match: Raúl Albiol (Villarreal)
"He demonstrated great leadership on the pitch, a real role model. He was very strong in the air and in one-on-one situations. He read the game with intelligence."
UEFA Technical Observer panel
Jordan Maciel, Bayern reporter
For 88 minutes, Bayern were in control of the match and looked the likelier team to progress to the semi-finals. But in the end, they were undone by a goal that epitomises their shortcomings this season. The competition top scorers they may be, but they have looked far too susceptible on the break – and have ultimately paid the price.
Delfín Ramírez, Villarreal reporter
Villarreal are back in the UEFA Champions League semi-finals for the second time in their history after a 16-year wait. A marvellous prize for a small-town team that has wonderful ideas about how to play the game.
Raúl Albiol, Villarreal defender: "We want more. We see ourselves as capable of causing all our opponents problems."
Unai Emery, Villarreal coach: "The [round of 16] game against Juventus gave us a lot of confidence and here it was another huge game, but the first leg already said a lot about us. We were perfect in defence."
Gerard Moreno, Villarreal forward: "We feel a lot of happiness. Ever since the draw paired us with Bayern, we have been telling ourselves that we could do it. The belief and the way this team competes has helped us to achieve it."
Thomas Müller, Bayern forward: "If you take just this game into account, without the first game, we should have gone through convincingly. It's difficult to accept this; I don't know what to say."
Julian Nagelsmann, Bayern coach: "The first leg was key – that's where we lost the tie. We didn't play well then; today we were very good. Tactically and intensity-wise, it was one of our best games in recent months."
Owen Hargreaves, BT Sport
"Villarreal were brilliant over two legs; they deserve it. Credit to Emery: he has the game plans to nullify some of the best players in the world."
- Villarreal are through to the Champions League semi-finals for only the second time – they lost 1-0 on aggregate against Arsenal in 2005/06.
- Bayern mustered 24 shots to Villarreal's four in Munich.
- Villarreal have lost only one of their last nine matches in the knockout phase of the Champions League (W3 D5).
- Top scorer Lewandowski hit nine goals in Bayern's five Champions League home games this season, compared to four away.
- Chukwueze's goal was only his sixth of the season in all competitions for Villarreal, and his first of 2022.
Lucas Hernández – 7
Raúl Albiol – 7
Samu Chukwueze – 6
Bayern: Neuer; Pavard, Upamecano, Hernández (Davies 87); Sané, Kimmich, Goretzka, Coman; Müller (Choupo-Moting 90), Musiala (Gnabry 82); Lewandowski
Villarreal: Rulli; Foyth, Albiol, Pau Torres, Estupiñán; Parejo (Aurier 90+3), Capoue, Coquelin (Chukwueze 84); Gerard Moreno, Danjuma (Pedraza 82), Lo Celso
Villarreal will face Liverpool in the semi-finals. The first leg takes place at Anfield on 27 April, with the second leg in Spain on 3 May.