The young La Masia graduate was on target for both the game's goals after being teed up by Lionel Messi for the opener, as the other two members of MSN enjoyed a night off
The holders had done most of the hard work against their city rivals by claiming a 4-1 victory in the first leg at Camp Nou.
Lionel Messi did the damage in that game with a double in a contest in which Espanyol were reduced to nine men.
And it was Messi - fresh off winning his fifth Ballon d'Or earlier this week - who played a starring role at Cornella-El Prat.
Messi provided Barca's main threat in front of goal in the first half and, although he was unable to find the net, he did set up Munir in the 32nd minute with a magnificent pass.
With a place in the last eight all but secured, Barca took their foot off the gas in a low-key second half but were still able to make it two with a second from Munir despite replays indicating both he and Aleix Vidal had been offside during a free-flowing move.
Messi was the first to test Espanyol goalkeeper Francesco Bardi, who parried away the Argentina forward's volley from just inside the area in the 11th minute.
It was Messi who pulled the strings for much of the first half and he went close to opening the scoring in spectacular fashion 23 minutes in, surging towards goal and unleashing a left-footed curling effort only to be denied by a fine diving save from Bardi.
Barca finally broke the deadlock nine minutes later as Munir raced onto a perfectly weighted throughball from Messi and rounded Bardi to tap into the empty net.
Espanyol would have levelled shortly before half-time if not for Barca keeper Marc-Andre ter Stegen.
Ter Stegen tipped Felipe Caicedo's dinked effort over after the Ecuadorian had been put through one-on-one with the German.
Caicedo got in behind the Barca defence again nine minutes into the second half only for Ter Stegen to leave him frustrated once more by sticking out a leg to preserve the visitors' advantage.
Following that opportunity clear openings proved few and far between in the second 45 minutes as Barca sought to preserve energy.
But there was still time for one final flourish from Barca as Messi and Arda Turan combined to play in Vidal who - with the flag staying down - squared for Munir to convert with a simple finish.