Messi handed Coutinho the ball and the Brazilian playmaker converted the spot kick, ending a run of poor form.
Sevilla nearly equalised but goalkeeper Jasper Cillessen produced a brilliant save from Andre Silva’s backheel, before the Dutch goalkeeper palmed away Ever Banega’s penalty kick
Gerrard 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.
Two goals in a two-minute spell after the break helped FC arcelona race ahead, with Coutinho heading in from Luis Suarez’s cross and Sergi Roberto tucking home a ball from Messi.
Guilherme Arana pulled a goal back for Sevilla with a powerful drive after the otherwise impressive Cillessen gave the ball away.
But Pablo Machin’s side were finally sunk when Suarez struck on the break and Messi added a late sixth.
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.