Madrid, Spain - Chelsea came agonizingly close to achieving a miracle in Madrid as it led Real Madrid 3-0 at one point, only to see the Karim Benzema, who struck a hat-trick in London, haunt it again with a goal late in extra time, giving the Spanish side a 5-4 aggregate triumph despite a 3-2 loss on the night.

The Blues came close to one of the all-time great Champions League comebacks in the Santiago Bernabéu as Mason Mount and Antonio Rüdiger, with a towering header, levelled the tie in the absence of the away goals rule.

Marco Alonso's goal was then ruled out before Timo Werner skipped past two defenders on the left and found the net with a deflection in the 75th minute.

Real hit back immediately, with a stunning outside of the foot pass from Luka Modrić finding substitute Rodrygo, who volley home with almost his first touch.

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That took the game to extra time and Vinicius crossed for Benzema to bullet home a header in the 95th minute. In the end, Madrid somehow did enough to progress as they held out against a last few frantic attacks.

"Not many teams can come here and dominate them like we did," Rüdiger told BT Sport. "But then their individual class came to light, and now we are here."

"It is unbelievable. We were dead until the goal we scored," Modrić said. "In this competition, experience helps, but for me Chelsea are the most difficult to play against."

"But we showed great character and desire. It is a defeat that feels very sweet."

The record champions could play city rivals Atlético Madrid in the other semi if Diego Simeone's men can salvage a 1-0 deficit to Manchester City.

Meanwhile, Samu Chukueze scored two minutes from time for Villarreal to stun Bayern Munich and send the Bundesliga giants crashing out of the Champions League quarter-finals.

Chukueze finished a slick counter-attack to rescue a 1-1 second leg draw for Villarreal in Munich, a week after a 1-0 win at home, to reach the last four for the second time in its history.

Robert Lewandowski had levelled the tie on aggregate early in the second half but Bayern could not find a winner and were hit by a sucker punch.

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Bayern boss Julian Nagelsmann told Amazon Prime Video the previous defeat "was the key, we lost the duel there."

"If you take just this game into account, without the first game, we should have gone through convincingly," attacker Thomas Müller said. "It's difficult to accept this. I don't know what to say."

Villarreal's players understandably ecstatic. "Ever since the draw paired us with Bayern, we have been telling ourselves that we could do it," striker Gerard Moreno insisted.

"The belief and the way this team competes has helped us to achieve it."

Unai Emery's "Yellow Submarine" is now in the semi-finals of the elite continental competition, having won the Europa League last season.

The ultimate underdog will meet the winner of Liverpool vs. Benfica, with the Reds defending a 3-1 lead at Anfield.