Sevilla, 2-0 winners in the first leg, went behind through Philippe Coutinho’s penalty, before Ever Banega had a spot-kick saved by Barca’s Jasper Cillessen.
Ivan Rakitic prodded in a second, Coutinho headed in a third and Sergi Roberto gave Barca a 4-2 overall lead.
Guilherme Arana pulled one back for Sevilla, but fine team goals from Luis Suarez and Lionel Messi sealed the win.
It finished 6-1 in the second leg at the Nou Camp, as the holders completed a 6-3 aggregate victory to join Valencia and Real Betis in the final four.
In the fourth quarter-final, Real Madrid travel to Girona on Thursday, leading 4-2 from the first leg.
How the goals went in
- 1-0, Coutinho (Barcelona, 13 mins). Messi goes to ground under a challenge from Quincy Promes, the away players claim Messi kicked the ground instead of there being contact, but the referee gives the penalty and Coutinho drilled it past Juan Soriano.
- Missed penalty, Banega (Sevilla, 26 mins). Gerard Pique brings down Roque Mesa, but Cillessen dives to his left to make a fine save from Banega’s penalty.
- 2-0, Rakitic (Barcelona, 31 mins). Five minutes after Sevilla’s missed penalty, Arthur plays a through ball and Rakitic manages to get a toe to it to prod it past Soriano.
- 3-0, Coutinho (Barcelona, 53 mins). Suarez crosses from the right and Coutinho, sprinting towards the near post, gets in front of his marker and heads in.
- 4-0, Sergi Roberto (Barcelona, 54 mins). Messi slides a perfectly-weighted ball into the path of Roberto and he slots it past Soriano.
- 4-1, Arana (Sevilla, 67 mins). Cillessen’s misjudged clearance falls to a Sevilla player and eventually it comes to Arana, who shoots into the net.
- 5-1, Suarez (Barcelona, 89 mins). With Sevilla needing one goal to go ahead on away goals, they push men forward for a corner, but a Barcelona counter-attack sees Suarez tap in from Jordi Alba’s cross.
- 6-1, Messi (Barcelona, 93 mins). Messi completes a fine one-touch passing move involving four players to seal the victory.
Elsewhere on Wednesday, Betis beat Espanyol 3-1 after extra time to complete a 4-2 aggregate victory.