Published: 2019-01-31 05:18:50 BdST
After a 2-0 defeat in Seville last week in which they rested key players, the Catalans broke the deadlock in the 13th minute when Coutinho slotted home from the penalty spot following Quincy Promes's foul on Lionel Messi.
Messi handed Coutinho the ball and the Brazilian playmaker converted the spot kick, ending a run of poor form.
Gerard Pique fouled Roque Mesa and after a long delay while the incident was checked by VAR, Argentina midfielder Banega fired to the goalkeeper's left, but Cillessen flew across to keep the ball out.
Barcelona pulled the game level on aggregate in the 32nd minute when Ivan Rakitic nudged the ball past Juan Soriano with the faintest of touches after a sensational pass from Arthur.
Two goals in a two-minute spell after the break helped Barcelona race ahead, with Coutinho heading in from Luis Suarez's cross and Sergi Roberto tucking home a ball from Messi.
Earlier Real Betis, whose Benito Villamarin stadium will host the final in May, beat Espanyol 3-1 at home after extra-time to progress 4-1 on aggregate.
Leo Baptistao headed Espanyol in front after 33 minutes but Giovani Lo Celso equalised in the 76th minute before Marc Roca was dismissed for the visitors.
Betis capitalised on their numerical advantage in extra-time, with Sergio Leon and Aissa Mandi's strikes earning them a semi-final spot.