Early goals from Luis Suarez and Lionel Messi calmed the nerves at the Nou Camp after Barca's great rivals Real Madrid, as well as Athletic Bilbao and Real Sociedad, had been knocked out of this season's competition by unfancied opponents.
Facing city rivals Espanyol was a potential banana skin for Ernesto Valverde’s side, who lost last week's first leg 1-0, but Barcelona were rarely troubled in front of a vibrant Nou Camp.
His every touch was loudly cheered on a night when Barca bade farewell to their versatile Argentine Javier Mascherano who is joining Chinese Super League side Heibei China Fortune.
Mascherano was given a guard of honour before the game in recognition of his seven-and-a-half years at the Nou Camp.
Espanyol produced a spirited late comeback but were almost caught on the break when Messi headed against the post.
Barca join Real Madrid's conquerors Leganes, Valencia, who on Wednesday beat last season's runners-up Alaves on penalties, and Sevilla, who thrashed Atletico Madrid, in Friday’s draw for the semis, with the first legs to be played next Wednesday.