Spanish trio and Sporting reach Europa semis
Sporting completed an all-Iberian line-up by knocking out Metalist Kharkiv, who missed a penalty in a 1-1 draw in Ukraine allowing the Portuguese side go through 3-2 on aggregate.
Athletic, Manchester United's conquerors in the previous round, played more of the entertaining football which is a hallmark of their eccentric coach Marcelo Bielsa as they drew 2-2 at home to Schalke 04 to qualify 6-4 on aggregate.
Atletico Madrid won 2-1 at Hannover 96 with an 87th-minute winner from Radamel Falcao, last season's top scorer in the competition playing for champions Porto, to complete a 4-2 aggregate win.
Adil Rami scored two early goals to set Valencia on their way to a 4-0 victory over AZ Alkmaar as they comfortably overturned a first-leg deficit to win 5-2 on aggregate.
Spain also has Barcelona and Real Madrid in the last four of the Champions League and there is now a possibility that both European finals this season will be all-Spanish affairs.
Atletico Madrid face Valencia in the semi-finals while Athletic Bilbao, enjoying their best European campaign since reaching the final of the old UEFA Cup in 1977, play Sporting.
The showpiece will be staged in Bucharest on May 9 where an Athletic-Atletico final would pit Bielsa against Diego Simeone, who played under him for nearly four years with Argentina, on the touchline.
Leading 4-2 after their impressive win in Gelsenkirchen, Bielsa's Athletic side, 11th in La Liga, did it the hard way, twice coming from behind against the Bundesliga's third place team.
Bielsa, who has also coached Chile, watched the game in his unmistakable manner, either pacing incessantly up and down the technical area or crouching on his knees.
His nerves were on edge when Dutchman Klaas-Jan Huntelaar put Schalke ahead in the 29th minute with a low drive from the edge of the area, but Ibai Gomez levelled four minutes before the break at a typically exuberant San Mames.
Former Real Madrid and Spain striker Raul put Schalke back in front with a left-foot strike from 25 metres in the 52nd minute, giving the Germans renewed hope of an unlikely fightback.
It was short-lived, though, as Markel Susaeta burst forward to fire the equaliser three minutes later.
Atletico, Europa League winners two seasons ago, took a 2-1 lead to Germany and were happy to sit back until the 63rd minute when Adrian Lopez pounced to score a fine individual goal.
Mame Biram Diouf brought Hannover back into contention with an 81st-minute equaliser but striker Falcao settled the match three minutes from time.
The Colombian striker, who hit a competition record 17 goals last season, cushioned Diego's pass on his chest and thumped home an emphatic finish to the delight of Atletico coach Simeone, wearing his customary all-black outfit.
Former UEFA Cup winners Valencia were the only team who managed to overturn a first-leg deficit, needing only 17 minutes to take control against an Alkmaar side who are second in the Dutch league.
Frenchman Rami struck after 15 minutes, beating Esteban Alvarado to Sofiane Feghouli's cross, and scored again from close range two minutes later after Roberto Soldado flicked on Tino Costa's cross.
Jordi Alba and Pablo Hernandez completed the rout after half-time.
Ricky van Wolfswinkel headed Sporting in front just before half-time at Metalist, who hit back with a Jonathan Cristaldo goal in the 57th minute.
Seven minutes later, Metalist blew a chance to level the aggregate score when Cleiton Xavier's penalty was saved by Rui Patrico.