There was no stopping Barca, with both Daniele De Rossi and Kostas Manolas both unfortunate to turn the ball into their own net, ahead of a goal from Gerard Pique.
Edin Dzeko did manage to pull a goal back for Roma, but Luis Suarez killed off the tie with his late strike.
Barca had to be alert early on with Jordi Alba doing well to clear a Diego Perotti cross with Alessandro Florenzi lurking.
Suarez was offside as he turned home an Andres Iniesta pass on seven minutes, before Roma goalkeeper Alisson was forced to palm a fierce Lionel Messi shot.
Suarez saw a shot deflect off target ahead of an effort against a post from Ivan Rakitic as Barcelona probed for an opener.
Alisson did well to divert a Suarez shot from a Messi flick forward, as Iniesta fired over the Roma goal just past the half-hour mark.
The Barca pressure paid off though as De Rossi slid in to win the ball ahead of Messi inside the box, but could only direct the ball home.
Perotti should have done better with a header at the start of the second period that he diverted wide, while Suarez could only fire over as the ball dropped to him as Alisson dropped Alba’s long-range drive into his path.
It went from bad to worse for Roma though as Manolas then also steered the ball into this own net, with ten second-half minutes played.
Rakitic smashed a cross across the face of goal following a short corner with Messi, leaving Umtiti to fire home, although his shot hit a post and then Manolas before rolling over the goalline.
Pique soon had Barca in an unassailable lead, with a tap-in from close range after Alisson had denied Suarez.
Alba did well to block an Aleksandar Kolarov shot as the away side looked for a way back into this tie.
Pique blocked a goalbound effort from Kevin Strootman, and while the Italians threatened through Gregoire Defrel late on, he was denied by an excellent stop by Marc-Andre Ter Stegen.
Dzeko though was able to hit a goal for Roma, with ten minutes to play, with a neat finish from a pass from Perotti.
However, Barca had the final say as Suarez scored the final goal of this game, as Denis Suarez’s low cross rebounded off Fazio and into his path for an easy finish.