It was a significant let-off for Juventus and they were forced to sit deep as Barca continued to create chances with Neymar and then Sergi Roberto - their matchwinner against PSG - volleying over.
Quite surprisingly, Lionel Messi side was restricted to one shot on target earlier today.
Juve's Gonzalo Higuain fired tamely at Marc-Andre ter Stegen and Juan Cuadrado missed another chance but the final whistle was celebrated wildly by the champions of Italy, who have not conceded a single goal from open play in this season's Champions League.
"Overall they were the better team and deserved to go through", he told BeIN Sports Spain. "At the start of the season not many people would have thought the team would do this well, or that I would", said Falcao, who has fought back from disappointing loan spells with Manchester United and Chelsea following a serious knee injury.
"It was a hard result to turn around, although we tried until the end". But they also put on a great defensive performance - the art of defending and game management was on fully display for the millions watching around the world to see.
Lionel Messi, Neymar and Luis Saurez all had chances that they squandered, so there is no doubt Juventus benefited from good fortune.
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Juventus right-back Dani Alves has revealed the advice he gave to a sobbing Neymar in the aftermath of Wednesday's 0-0 Champions League quarterfinal second-leg tie with Barcelona.
Juve go into today's semifinal draw along with Real Madrid, Monaco and Atletico Madrid - all of whom have faced Massimiliano Allegri's men in recent European campaigns.
It is 21 years since Juventus won the Champions League and they must be considered contenders.
"My players were extraordinary tonight".
Jardim added in a press conference: "There are now three great teams (in the draw) with a lot of experience. They kept their cool".
Barca coach Luis Enrique had said before Wednesday night's game that his side would attempt to overturn the 3-0 deficit from the first leg until the very last minute of the return leg in front of their own fans and he was true to his word, reports Xinhua news agency. "I'll keep remembering that first half at Juventus Stadium". Having now avenged their 2015 Champions League final loss to Barcelona, Juventus also leads the Italian league and has lined up an Italian Cup final against Lazio. His side travel to face eternal rivals Real Madrid in El Clasico on Sunday realistically needing to win to maintain their hopes of a third straight La Liga title.