Many thought that the Spanish side were as good as through following their 4-1 first leg victory, but the Italians shocked the world with a sensational performance at the Stadio Olimpico.
Edin Dzeko got the hosts off to a dream start early on as he latch onto a beautifully-weighted ball from Daniele De Rossi to bring the ball under his spell with his chest, hold off his marker and stab beyond Marc-Andre Ter Stegen to open the scoring.
April 10, 2018
From that moment on it felt like there was something in the air in Rome as the hosts dominated the game creating a plethora of chances.
Patrik Schick - making his Champions League debut - had a glorious chance to make it two as he met Federico Fazio's cross from the right unmarked eight yards out but he could only head wide of the far post with Ter Stegen rooted to the spot.
A wonderful challenge from Gerard Pique denied Schick a clear opening shortly afterwards before Dzeko saw a far-post header well tipped over after meeting Alessandro Florenzi's looping cross from the right.
Despite their chances Roma went in at the break needing two more goals to progress, but they clearly weren't disheartened.
- Pique gift -
Just before the hour-mark Dzeko - who was a thorn in Barca's side all night with his physicality and hold-up play - did brilliantly to hold off Pique, with the centre-back only able to trip his man as he made a last-ditch effort to deny him a clear strike on goal. After a moment's hesitiation the man in the middle pointed to the spot and De Rossi assumed responsibility, keeping his cool to slot beyond Ter Stegen and into the stanchion despite the German guessing correctly.
April 10, 2018
The visitors were incesnsed shortly afterwards as Fazio escaped a second yellow card for a clumsy challenge on Andres Iniesta and Roma took full advantage of that let-off.
Radja Nainggolan saw a low volley kept out by Ter Stegen after being fed by fellow midfielder Kevin Strootman, before De Rossi flicked a header narrowly wide at the far post.
The hosts could have been forgiven for thinking it was going to be a case of so near but so far when substitute Stephan El Shaarawy saw an effort at the far post beaten away by Ter Stegen shortly after being introduced but with just eight minutes to play, Roma's persistence paid off.
- Late scenes -
A corner was swung in from the right and Manolas got a run on his man to meet it at the near post and flick a header beyond a rooted Ter Stegen and into the far corner to spark scenes in the Italian captial.
To put the scale of their achievement into perspective, Barcelona had only conceded three goals in the entire competition before Tuesday's game, only to see that tally double in the space of 90 minutes.
The Greek was called into action at the other end in the closing stages as he made two exquisite late blocks to deny Barca.
Substitute Ousmane Dembele almost played the role of party pooper as he curled an effort onto the foor of the net after Alisson had raced out to smother a Gerard Pique-led break, but a sucker punch would have been incredibly harsh on the hosts, who more than deserved to progress on the balance of play.
The Olimpico erupted once again as the full-time whistle went and Roma's place in the last four of Europe's premier club competition was confirmed, the first time the club have reached the semis since 1983/84.
Are you not entertained?! Is this not why you are here?!
— AS Roma English (@ASRomaEN) April 10, 2018
FT | #RomaBarca 3⃣-0⃣ (4-4 - Roma win on away goals) pic.twitter.com/9JjrofW1pp