Barca trailed 1-0 from the opening leg after Oscar Melendo's late finish, but there was little danger of Ernesto Valverde's men following Real Madrid in crashing out of the tournament.
Almost 80,000 fans at Camp Nou waved goodbye to Javier Mascherano pre-match, and Barca made a terrific start in the Catalan derby - Luis Suarez swiftly erasing the first-leg deficit with a header from a fine right-wing Aleix Vidal cross.
Espanyol wasted chances to reclaim the initiative and Messi came up with the key goal, although his shot needed a touch off Naldo to wrongfoot goalkeeper Pau Lopez, before Coutinho was introduced by Ernesto Valverde for a bright 22-minute cameo.
Messi hit the post late on, but Barca - winners of the Copa del Rey in each of the last three seasons - remain in with a chance of matching the four straight titles won by Athletic Bilbao in the 1930s.
With both Real and Atletico Madrid having gone out in the quarter-finals, Barca will now compete with Sevilla, Valencia and Leganes for a place in the Copa del Rey showpiece. The draw for the semi-finals will be made on Friday.
Barca needed only eight minutes to get level on aggregate, surprise starter Vidal sent clear by Messi to provide a perfect cross for Suarez to head home at the back post, the striker's eighth goal in his last six appearances against Espanyol.
But Espanyol immediately fired a warning shot of their own, Gerard Moreno shooting straight at Jasper Cillessen after being picked out by Sergi Darder.
The visitors continued to threaten and Esteban Granero should have hit the target from a Victor Sanchez cross, the former Real Madrid man sending his first-time shot wide.
Barcelona punished that error by taking the lead in the tie after 25 minutes, scoring their 4,000th goal in official competitions at Camp Nou.
Persistence from Vidal won the ball on the edge of the Espanyol box, with Messi driving into space and hitting a firm 20-yard strike that beat Lopez with the aid of a deflection off Naldo.
Messi missed a chance to put the tie beyond Espanyol just before the break, brushing the side netting after Andres Iniesta sent Jordi Alba clear down the left to deliver a low cross.
Lopez denied Messi a second with a fine save after 55 minutes before record signing Coutinho - wearing Mascherano's old number 14 shirt - was introduced for his Barca bow.
With Quique Sanchez Flores' men committing more men in attack, Barca were increasingly dangerous on the break and Lopez had to make a superb double save from Suarez and Ivan Rakitic after Messi had played Coutinho into space on the left.
Espanyol were only ever a goal away from shocking Camp Nou but Moreno's hopeful penalty appeal after a tangle with Alba on the edge of the box was the closest they came as Coutinho's debut - against the club he represented on loan in 2012 - ended in a Copa derby victory, with Messi thumping a header against the post with two minutes left, denying him a deserved final word.