Two own-goals, from Daniele De Rossi and Kostas Manolas, and a close-range finish from Gerard Pique, presented the Catalans with a flattering 3-0 advantage at the Camp Nou before Edin Dzeko snatched Roma a late away goal.
But, just as the Italians looked to have grabbed a lifeline, Luis Suarez restored the three-goal cushion, by scoring a fourth in the 87th minute.
It means Barca will head to Italy next week with a place in the last four firmly in their grasp but this was not a virtuoso attacking display.
Instead, they benefited from two fortuitous own goals and some careless Roma finishing. They are unlikely to meet as generous an opponent in the semis.
“We did not that have continuity in the game,” Valverde said. “We had some errors and there were times that we rushed into the attack, instead of having some control.”
Barca also had referee Danny Makkelie to thank for not awarding Roma an early penalty, after Nelson Semedo pushed Dzeko in the back.
Poster boy: Lionel Messi holds a framed poster celebrating his 100th Champions League goal ahead of Wednesday’s game
“They are already good on their own, they don’t need help,” Roma coach Eusebio Di Francesco said.
“Tonight they had help both from the referee and from us.”
After Cristiano Ronaldo’s spectacular bicycle kick for Real Madrid on Tuesday, even Lionel Messi, back from injury, endured a slightly frustrating night, his shots and dribbles for once meeting opponents rather than the net.
Messi returned to the starting line-up after recovering from his hamstring complaint, as did Sergio Busquets, back after breaking his toe against Chelsea three weeks ago.
But while Messi completed the 90 minutes seemingly unscathed, Busquets had to be replaced by Paulinho midway through the second half.
“Busquets has played with some small discomfort for the injury he has,” Valverde said. “In the end he was suffering a lot and we have changed it, but that’s fine.”
Barca led at half-time after De Rossi slid to prevent Andres Iniesta’s pass reaching Messi and inadvertently stabbed into his own net.
Two goals in four second-half minutes then took the tie away from the visitors as Samuel Umtiti’s finish cannoned off both the post and then Manolas, before Pique sidefooted home from close range.
Dzeko’s finish might have given Roma hope had it not been cancelled out by Suarez scoring a fourth, as Barca wrapped up a win that did not wholly reflect a scrappy performance.
“The truth is we know that in the game we can and we must improve in several points,” Barca’s Ivan Rakitic said.
“But we’re very happy for the work. When maybe you’re not playing at 100 per cent, you have to stay together, to be strong. 5-1 would be better than 4-1, to be more calm, and we know Roma will try to turn it around.”
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