Valencia fought back from a three-goal, first-leg deficit Thursday to beat Basel 5-0 and qualify for the Europa League semifinal, while competition favorite Juventus advanced after a tense 2-1 win at home to Lyon.
Pablo Alcacer scored a hat trick in Valencia, with the third coming in extra time after Basel's Marcelo Diaz and Gaston Sauro were sent off.
Eduardo Vargas and Juan Bernat also scored to help Valencia become the first side to come back from a 3-0 first leg defeat and progress in the Europa League.
"I'd like to thank my teammates, without whom I wouldn't have scored this hat trick tonight," Alacer said. "The fans were with us from the very first minute tonight; they were fantastic and we dedicate this win to them."
In Turin, Andrea Pirlo and Claudio Marchisio scored either side of Jimmy Briand's leveler for Lyon, handing Juventus a 3-1 aggregate win. Marchisio's strike was later awarded as an own goal by UEFA, after it took a decisive deflection off Samuel Umtiti.
"We hope that the whole of Italy is happy with our result," Juventus coach Antonio Conte said. "In Italy you're either a Juventus fan or against Juventus. And those who are against us don't care a lot about the UEFA ranking and only hope that we are knocked out.
"We are proud and happy. Three years ago we didn't even qualify for the Europa League, in the last two years we have done a lot and won a lot and this year we are protagonists too. The fans shouldn't forget that."
Benfica, beaten by Chelsea in last season's final, could be back in the showpiece match next month after beating AZ Alkmaar 2-0 to seal a 3-0 aggregate victory, while 10-man Sevilla defeated Porto 4-1 to qualify 4-2 on aggregate.
Basel had seemed certain to progress after a comfortable win in Switzerland, but two goals shortly before halftime gave Valencia hope.
First Alcacer chested down Joao Pereira's ball over the defense and fired it into the bottom left corner, before Vargas headed home Dani Parejo's corner.
The two goalscorers combined in the 70th minute with a delightful cut back from Vargas to the onrushing Alcacer, who lashed the ball into the top left corner to level the tie.
Basel goalkeeper Yann Sommer kept his side in the tie with a number of stunning saves, while counterpart Vicente Guaita saw little of the ball.