Copa del Rey holders Barcelona had to weather a first-half storm from Athletic Bilbao before progressing to the semi-finals for the seventh consecutive season with a 3-1 win to seal a 5-2 aggregate victory.
Atletico Madrid failed to make the last four, though, as they conceded three goals for the first time in a year to lose 3-2 on the night and on aggregate to Celta Vigo.
Inaki Williams's early strike for the visitors at the Camp Nou gave Athletic hope of exacting revenge for defeat in last season's final to Barca.
However, the Basques failed to take a series of chances when on top before half-time and Barca responded in
the second period thanks to goals from Luis Suarez, Gerard Pique and Neymar.
"The early goal for them made life difficult for us," Suarez told Canal Plus.
"We know we didn't play well in the first-half, but in the second-half we came out with a different attitude and that allowed us to save the day and progress to the semis."
Williams signed a new long-term deal with a 50 million euro buyout clause last week and showed more signs of his burgeoning talent with a cool finish from Aritz Aduriz's fine through ball to register his 11th goal of the season.
Athletic should have then gone in front on aggregate when Javier Eraso turned Williams's dangerous cross wide before Markel Susaeta also failed to hit the target from Aduriz's knockdown.
Those misses were to prove crucial as Barca upped their game after the break as the star front three of Lionel Messi, Suarez and Neymar came alive.
Messi created the equaliser when he latched onto Sergi Roberto's ball over the top and his low cross was slotted home at the back post by Suarez for his 30th goal of the season.
Pique killed the tie off nine minutes from time when he rose to power home Dani Alves's cross from the right.
And Neymar got his revenge for some rough treatment dished out by the Athletic defence when he skipped past Mikel San Jose before firing into the corner.
Barca meet Atletico in a top of the table clash in La Liga on Saturday, but there is no chance of the sides meeting in Friday's semi-final draw as Celta produced an upset at the Vicente Calderon thanks to Pablo Hernandez's brace either side of former Manchester City and Celtic striker John Guidetti's sensational strike.
"To come to such a great stadium and club and play such an all-round game with bravery and character, playing our style of football, I am proud to coach these players," said Celta boss Eduardo Berizzo, who hailed the result as his best in charge of the Galicians.
"We didn't play badly. We created plenty of chances, but it is true we made mistakes in the small details of the game and they took advantage of it," said Atletico coach Diego Simeone.
Following a 0-0 draw in the first-leg last week, Hernandez handed Celta the vital away goal when he headed home the opener midway through the first-half.
Antoine Griezmann gave the 10-time Cup winners hope with an equaliser before half-time.
But Guidetti's stunning hit into the top corner from 25 yards and another Hernandez header sealed the Galicians a place in the semi-finals before Angel Correa's late consolation.
Gary Neville's Valencia look to kick start their stumbling campaign when they face Las Palmas on Thursday after only managing a 1-1 draw in the first-leg at home last week.
And Sevilla are heavy favourites to make the last four as they carry a 2-0 lead into their second-leg away to Second Division Mirandes.