Atletico will face city rivals Real in the last four after beating Athletic Bilbao 2-1 in their second-leg meeting, 3-1 on aggregate, while Barca won 5-1 on the night to set up an aggregate 9-2 success.
Diego Simeone's side booked a repeat of last season's final after coming from a goal down with two second-half strikes to inflict Bilbao's first defeat at the new San Mames.
Aritz Aduriz opened the scoring for the hosts in the 42nd minute, which put Bilbao level in the tie, however Raul Garcia levelled for the holders 10 minutes into the second half.
That away goal all but sealed Atletico's progression, but they secured victory on the night as Diego Costa ended a run of seven games without a goal in all competitions with an 86th-minute winner.
Fellow La Liga title challengers Barcelona also made it through to the last four with a comprehensive victory over Levante.
The visitors went ahead at Camp Nou in the ninth minute through an unfortunate own goal from Sergi Roberto, the youngster unaware as a Levante header struck him on the back to divert the ball into the net.
It was the third consecutive meeting with Barca that Levante had taken the lead, but just like previous games they were not ahead for long as Adriano levelled 19 minutes later with his third goal of the season from 20 yards.
Carles Puyol then put Barca in front with a powerful front-post header from a Cristian Tello corner, the defender's first goal in over a year, before Alexis Sanchez struck twice in as many minutes at the start of the second half to make it 4-1.
Cesc Fabregas completed the scoring in the 68th minute, the midfielder cutting in from the right before driving a low shot beyond Javi Jimenez to set up a semi-final against the winner of Real Sociedad and Racing Santander, who play on Thursday.
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