Alternatively, Monaco stunned Borussia Dortmund to head into the semi-finals alongside Juventus, Real Madrid and Atletico Madrid.
There were mixed emotions for Dani Alves after the Juventus fullback helped shed former team Barcelona from the Champions League in the quarterfinals.
Juventus could be one of the major favourites for the 2016-17 Champions League trophy.
A better chance went begging a few moments later when Messi lashed a left-footed strike wide from 15 yards after Luis Suarez's flick had set him up. They're Italian and they defended very well. Monaco are the dark horse of the competition, while all the teams in the pot would like to avoid Juventus in the last four. On Sunday we have a big game - it's the business end of the season.
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"We did very well defensively, less so in attack where we failed to make the most of very promising counter-attacks".
Gianluigi Buffon hopes the comprehensive win over five-times European champions Barcelona is a sign his side are ready to take the next step. I wish them the best until the final.
Otherwise, the same Juventus starting 11 from the first leg had control of the match, bending but never breaking under the assault of a Barcelona in full-attack mode.
"Aside from the result, the belief and character of our approach was excellent and it's a good confidence booster to qualify comfortably against what remains probably the best team in the world", Buffon added.
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Barca are in the final of the Copa del Rey but Enrique knows that even if his side beat Alaves on 27 May, it will be scant consolation if they fail to win La Liga following another disappointing European campaign.
Barcelona kept on trying, with Messi again going close and Sergi Roberto shooting just wide as to their vast credit Barcelona kept on pushing for a miracle which looked increasingly unlikely with every passing minute.
However, he believes they are far more equipped to win the Champions League for a third time than when they lost to Barca in the final two years ago.
Gonzalo Higuain missed two first-half chances inside the box for the visitors, while Barcelona's Lionel Messi also fluffed two of his own either side of the break as the hosts chased the game.
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With half an hour remaining and his side still needing three goals to force extra time, Barca coach Luis Enrique replaced midfielder Ivan Rakitic with striker Paco Alcacer, but the fact was that most of his side's efforts continued to be from outside of the penalty area. "It felt like the match could have gone on a lot longer without us conceding".