Atletico's battling 2-1 comeback victory in a rain-lashed quarter-final, second leg in the Basque Country, which made it 3-1 on aggregate, was Bilbao's first reverse at their new San Mames arena and meant Diego Simeone's side, who are joint top of La Liga and through to the last 16 of the Champions League, are still fighting on three fronts.
The heavens also opened over the Catalan capital as Barcelona fielded a second-string side against Levante at a Nou Camp stadium that was barely a quarter full and recovered from conceding an early goal to secure a 9-2 aggregate success.
The record winners, who have claimed Spain's domestic Cup 26 times, won 5-1 on the night after last week's 4-1 victory in Valencia in the first leg when they also fell behind.
Barca will play Real Sociedad or third-tier Racing Santander in the last four, although the Santander players have threatened to boycott Thursday's match in protest over unpaid wages.
Sociedad lead 3-1 from last week's first let at their Anoeta stadium in San Sebastian.
Atletico won the first leg against Bilbao in the Spanish capital 1-0 and Diego Costa came close to making it 2-0 on aggregate in the first minute.
Playmaker Koke sent the Brazil-born forward clear on goal but Bilbao goalkeeper Iago Herrerin sprinted off his line and saved Costa's low drive with his legs.
Roared on by their red and white-clad fans, the home side gradually seized the upper hand in an intense first half and were rewarded when Aritz Aduriz nodded into the corner from Mikel Balenziaga's cross in the 42nd minute.
Atletico goalkeeper Thibaut Courtois conjured three superb saves to deny Andoni Iraola, Aduriz and Mikel Rico in the leadup to halftime before Raul Garcia clipped Emiliano Insua's centre into the corner 10 minutes into the second half to make it 1-1 on the night and 2-1 on aggregate to the visitors.
Needing two goals to turn the tie around, Bilbao mounted waves of attacks but Atletico held firm and struck again four minutes from time.
Koke again sent Costa clear with another brilliantly executed pass that left the home defence floundering on the halfway line and he rounded Herrerin and tapped home.
"After we got the opening goal it gave us confidence, strength, commitment and intensity and we were able to win at a very difficult venue," Simeone told a news conference.
"This stadium is full of passion and you experience football in its purest form," added the Argentine, who has transformed Atletico into genuine contenders in Spain and Europe since taking over at the end of 2011.
Looking ahead to the semi-finals, he said the more times his side could play against Real and Barca the better.
"When you play against them you learn more, you improve more and you lose this complex you have about taking part in this match."
Atletico's 2-1 win in extra time in last year's final was at Real's own Bernabeu stadium and they appear to have their number this season as well after earning a 1-0 win there in La Liga in September.
Real went through to the two-legged semi-finals, which are next week and the week after, when they beat Espanyol 1-0 in Madrid on Tuesday for a 2-0 aggregate success.
Barca, who lead La Liga with Atletico and are also through to the Champions League last 16, fell behind to Levante in the ninth minute when a Loukas Vyntra header ricocheted into the net off home midfielder Sergi Roberto.
Adriano bent a fierce drive in from distance to level in the 28th minute and veteran captain Carles Puyol brought back memories of his winning goal for Spain against Germany in the semi-finals of the 2010 World Cup with a powerful header from a corner to make it 2-1 shortly before halftime.
Now 35 and approaching the end of a glittering career, Puyol's leap wasn't quite as high as the one in Durban three and a half years ago but the shaggy-haired centre back showed he can still inspire the team when needed.
Alexis struck twice early in the second half and Cesc Fabregas added a fifth in the 68th minute as Barca remained on course for a third Cup triumph in six years following successful campaigns in 2009 and 2012.
The final is on April 19 at a yet-to-be-determined venue.


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