Barca came into the game as the Goliath after a 4-1 first-leg win but fell apart to the Romans' brilliant display.
Just like Liverpool, Barcelona started its quarterfinal second leg with a three-goal advantage.
Current mood in Barcelona.
Even Guardiola said himself before the first leg that the way his City side play is ideal for Liverpool, and apart from a stirring first-half effort from City in the return game, the quarter-final proved exactly that.
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.
Liverpool's participation is already confirmed, with Juventus and Real Madrid and Sevilla and Bayern Munich facing off on Wednesday night to seal the final two spots in the draw.
Greek defender Kostas Manolas headed home the crucial third goal from a corner with eight minutes remaining, joining de Rossi in making up for scoring in his own net in the first leg of the quarter-final tie.
UEFA president Aleksander Ceferin in February said that video technology would not be introduced for European competitions next season, citing "lots of confusion".
Roma reluctantly sold Salah last June.
Now Salah's 39-goal haul this season is on a par with Barcelona forward Lionel Messi.
The former Manchester United manager declined to stay in the North West while two of his fiercest rivals, Liverpool and Man City, duked it out for a place in the semi-finals and instead flew to Italy.
"I don't want a side that rests on its laurels or thinks it doesn't matter how the game goes".
Just as they were at the Camp Nou, Roma were aggressive from the off, and Dzeko gave the home side a deserved lead after just six minutes, brilliantly bringing down De Rossi's clipped through ball, holding off Samuel Umtiti and poking the ball past Marc-Andre ter Stegen. "It's hard to accept this elimination because we had a lot of hope for this season and once again it (the Champions League) has escaped us".
What made I Giallorossi's victory even more notable was the fact that the Blaugrana, famed for their "tiki-taka", were forced into playing a direct style of football, as the desperation to break down the Serie A side became evident as the game progressed in the second-half.