Porto's downfall was partly self-inflicted after left back Alex Telles received a red card in the 27th minute following two senseless bookings in the space of 90 seconds, leaving the home side to play over an hour against the Serie A leaders with 10 men.
Despite holding Juventus at bay for 72 minutes, Porto's resolve was broken when Miguel Layun deflected Paulo Dybala's pass into the path of Pjaca who slammed a first-time effort past Iker Casillas.
Dani Alves made sure of victory two minutes later when he controlled Alex Sandro's cross with his chest before finishing calmly as Juventus, who are still in the Italian Cup, boosted their hopes of a maiden treble ahead of the second leg in Turin on March 14.
"We can be happy as it's a really good result, but to be honest after the first-half red card, we had to win this game," Juventus midfielder Sami Khedira told BT Sport.
"It's absolutely not over," he added. "We're happy with tonight but in three weeks we'll need to be careful as Porto are angry and have nothing to lose."
Juventus were expected to face a stern test in Portugal, but while they imposed themselves from the early stages and controlled the first half, Porto were content to remain deep and absorb pressure.
The visitors struggled to forge the clear openings that their dominance deserved, although the lively Dybala fashioned the best chance of the first half with a thumping effort from outside the box which grazed the post.
Telles's minute and a half of madness quashed any lingering Porto ambition and prompted coach Nuno Espirito Santo to withdraw striker Andre Silva -- scorer of four Champions League goals this season -- in response.
Juve boss Massimiliano Allegri left out Leonardo Bonucci from the squad, after the pair's dispute during Friday's victory over Palermo, and while Juventus were untested at the back, they missed the centre back's creativity and probing long balls.
The breakthrough eventually came from the bench, as Allegri introduced Pjaca and Dani Alves to offer dynamism and directness and the pair repaid their manager with goals to end Porto's 20-game undefeated home streak.
(Reporting by Ed Dove; Editing by Toby Davis)
