It finished 5-0 at the final whistle as Celta could not recover from an early shock and lost the tie 6-1 on aggregate.
The tie was delicately poised at 1-1 after a first leg in which Celta played extremely well against, admittedly, an under strength Barca team but Ernesto Valverde recalled the likes of Jordi Alba, Andres Iniesta, Luis Suarez and Lionel Messi for the return match and the Catalans blitzed their opponents with an utterly dominant first-half display.
Alba, who set up both of Messi's goals, got on the scoresheet in the 28th minute as Messi repaid the favour to put the win beyond doubt.
"Messi is the best player in history and the best in the world by a difference", Alba told reporters after the game.
Barca's new record signing Philippe Coutinho - out for three weeks with a thigh injury - was also present as the former Liverpool attacker met his new team-mates.
"As he adapts to our game, to the Liga, to European football. he requires a process of adaptation and we hope he can help us during the season".
Gerard Moreno then smacked the post as Espanyol continued to threaten on the break but he added a second before the break when Tono failed to clear by booting the ball against his goalkeeper allowing Moreno to score.
Suarez joined the party even before the half time whistle and capitalising on Pione Sisto's sloppy back pass, Suarez found the net for the fifth game running. Making the last eight will take some of the pressure off new coach Vincenzo Montella following Sevilla's painful 5-3 home loss to crosstown rival Real Betis in his Spanish league debut on Saturday.
Barely two minutes later, Messi had his second from yet another Alba assist, the Argentine placing a low shot into the same corner of Sergio's net after Barca's full-back picked him out near the penalty spot.