Barca came into the game as the Goliath after a 4-1 first-leg win but fell apart to the Romans' brilliant display.
Roma, fourth in Serie A and 21 points behind leaders Juventus, ripped into their visitors from the start, and like City against Liverpool, they got an early goal, Edin Dzeko brushing off weak tackles to prod home from close range.
Roma, on the other hand, have joined Liverpool in the Champions League semi-final draw which is due to take place on Friday April 13.
Current mood in Barcelona.
When you think about it, it is pretty remarkable that Roma have reached the semi-finals of the Champions League without Salah, who has been directly involved in 50 Liverpool goals this season.
Jurgen Klopp side made it 4-1 on aggregate 10 minutes into the second half with a clean Mohamed Salah strike, before Roberto Firmino scored the victor for the night to end the game 5-1 on aggregate.
While the Roma fans celebrated long into the night, the Spanish press composed their headlines and they weren't flattering to the vanquished.
And with Barca trying to hold on, Kostas Manolas got the crucial goal eight minutes from time with a glancing header, Roma edging through thanks to their away goal. "We all wanted to win the competition but only one can win", Valverde added. Not that I don't respect Roma, the absolute opposite.
Striker Dzeko also waxed lyrical about his side's tactics and said he played with more freedom alongside Patrik Schick in attack, with Radja Nainggolan, who missed the first leg with injury, behind them.
Jimenez's criticism of Messi is perhaps a little unfair, though, as he was involved throughout-according to Summerscales he had 61 touches of the ball, just six fewer than the commanding De Rossi managed, per Squawka Football-and frequently had to drop deeper to create for the team with Andres Iniesta struggling to do so himself. "They lost Salah and they are in the semis!"
The Giallorossi made them pay nearly immediately as Dzeko latched onto a glorious ball over the top from De Rossi and poked past Marc-Andre ter Stegen to open the scoring on six minutes.
And the club website enjoyed itself on Twitter too.
"I am happy for the coaches and for my team-mates", said the ultimate team player after the victory. The Champions League success might help speed up the stadium process - especially if Roma reaches the final in Kiev.