Early goals from Luis Suarez and Lionel Messi calmed the nerves at the Nou Camp on Thursday.
This was 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 FC Barcelona were rarely troubled in front of a vibrant Nou Camp.
Barca’s new Brazilian attacking midfielder Coutinho was given a standing ovation when he came on to take his bow in the second-half.
He had arrived from Liverpool this month for a club record fee of 142 million pounds (200.65 million dollars).
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.
Suarez levelled the score in the tie after eight minutes, nodding in Aleix Vidal’s cross from close range to put Barca ahead.
Then, Messi’s deflected effort from distance in the 25th ensured place in the last four.
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.
The first leg ties are to be played next Wednesday.