Real Madrid saw off a stirring Chelsea fightback to book their place in the Champions League semifinals following a 3-2 defeat after extra time in a scintillating second leg at the Santiago Bernabeu Stadium on Tuesday to go through 5-4 on aggregate.

Chelsea had looked on course to complete an astonishing comeback after taking a 3-0 lead in their quarterfinal second leg with goals from Mason Mount, Antonio Rudiger and an excellent individual effort from Timo Werner.

Yet the hosts came roaring back, with Rodrygo finishing from a superb pass by Luka Modric to level the tie 4-4 on aggregate and force extra time when Karim Benzema headed home to decide a remarkable encounter.

"It was another incredible night, what a sweet tasting loss," Modric told Spanish media Movistar Plus.

"We didn't give up until the end. Despite going 0-3, I don't think we played a bad game. Another night of suffering, but the important thing is that we have qualified."

Bayern Munich were stunned as Villarreal scored an 88th minute equalizer through substitute Samuel Chukwueze to snatch a 1-1 draw and reach the Champions League semifinals with a 2-1 aggregate win over the Germans 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.

Yet despite controlling the game they failed to score again.

Instead it was Villarreal, semifinalists in 2006, who netted against the run of play with Chukwueze beating goalkeeper Manuel Neuer with a left-foot effort to silence the home crowd.

"We feel a lot of happiness. Ever since the draw paired us with Bayern, we have been telling ourselves that we could do it," Villarreal forward Gerard Moreno said. "The belief and the way this team competes has helped us to achieve it."

"In the first leg we made the mistake of not finishing the tie, and all the comments serve as motivation for us. They made the mistake today of not killing us off and we took advantage of that."

"If you want to achieve something in this competition you need to beat the big teams," Villarreal's coach Unai Emery said. "We took the first step (in the last 16) with Juventus. With Bayern we analyzed the game well."

(With input from agencies)