The Spanish side, who overcame a 4-0 first-leg deficit in the previous round to beat Paris St Germain, will have to pull a similar trick out of the hat after being comprehensively outplayed in the quarter-final first leg.
Dybala fired Juve ahead in the seventh minute and added the second goal before the half hour while defender Giorgio Chiellini headed in the third early in the second half in another rousing Juventus performance.
It could have been worse for Barca as Gonzalo Higuain, usually Juve's most dangerous marksman, missed two chances that he would usually have snapped up.
Barca had 65 percent of the possession but were strangely ponderous in midfield and leaky at the back, where they could not cope with the pace and aggression of Mario Mandzukic or Juan Cuadrado on the flanks.
The match pitted Chiellini against Barcelona forward Luis Suarez for the first time since the infamous incident at the 2014 World Cup when the Uruguayan bit the Italian defender.
Juve, unbeaten at home in a European tie for four years, went straight on to the attack and Higuain wasted their first chance after three minutes with a poor close-range header from Miralem Pjanic's cross.
They needed another four minutes to go ahead when Cuadrado found Dybala who cleverly turned and curled a left-foot shot past Marc Andre ter Stegen.
The player known as the Jewel, often tipped to be Messi's natural successor, struck again 15 minutes later, meeting Manduzkic's low cross in his stride to beat Ter Stegen inside the near post with another left-foot effort.
That goal came just after Juve goalkeeper Gianluigi Buffon had made a superb save from Andres Iniesta in Barca's best first-half attack.
Barcelona made a more promising start to the second half as Messi rolled one effort wide from the edge of the area and Iniesta then fired wide.
Juventus were not finished, though, and, after Higuain squandered another chance by delaying too long over his shot, Chiellini outjumped Javier Mascherano at the far post to head in from a corner for the third in the 55th minute.
The hosts kept attacking to the end and former Barca player Dani Alves had a chance to add a fourth but took too long over his shot.
(Writing by Brian Homewood; Editing by Clare Fallon)
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