The Italian champions entered the second leg holding a 2-0 lead from the reverse match in Porto, and Paulo Dybala's first-half penalty made it a comfortable progression into the last eight for Massimiliano Allegri's side.
As expected, Leonardo Bonucci started for Juventus after missing the first leg following a disagreement with head coach Allegri. Giorgio Chiellini, however, was only deemed fit enough for the bench due to a muscular problem.
As for Porto, Alex Telles was suspended after picking up a red card in the first leg, which opened up a spot in the team for Miguel Layun. Oliver Torres and Andre Andre, meanwhile, were also handed starts by head coach Nuno Espirito.
Twice Juventus had opportunities to make the breakthrough in the opening three minutes, but Higuain headed wide of the post from outside the Porto box, before Dybala fired over the crossbar from close range after breaking through.
Dybala had another shooting chance for Juventus in the seventh minute after finding a yard of space outside the Porto box, but the Argentine's effort just moved wide of the far post.
Mandzukic was next to come close for Juventus in the 23rd minute after meeting a cross from Juan Cuadrado, but the striker's header was saved by Iker Casillas, who kept hold of the ball under pressure from Higuain.
Clear opportunities were few and far between in the opening 40 minutes of action, but the first period ended on a high for Juventus and a real low for Porto, who had experienced defender Maxi Pereira sent off for stopping a goal-bound Higuain strike with his hand.
Indeed, the referee was quick to point to the penalty spot and it was Dybala that stepped forward to send Juventus ahead with a spot kick as the Italian champions took a 3-0 aggregate lead.
Both managers made alterations at the interval, with Marko Pjaca taking the place of Cuadrado, while Willy Boly was introduced for Porto in place of the highly-rated Andre Silva, who struggled in the opening 45 minutes.
Porto had a chance to level the scores in the 49th minute when Soares's pace took him clear of the Juventus defence and into a shooting position, but the striker could only curl his effort wide of the far post.
Juventus had a couple of opportunities to add gloss to the scoreline past the hour mark, but Higuain could only fire wide of the post after dancing into the Porto box, before Pjaca saw his effort evade the away side's goal.
Dybala was next to come close for the home side 20 minutes from time after meeting a cross from Alex Sandro, but the striker got his volley all wrong and the ball went harmlessly wide of the Porto post.
The majority of Porto's threat in the second period came on the counter-attack as they looked to give their supporters something to cheer, although it was Juventus that remained in control from start to finish.
Tomas Rincon replaced Dybala in the 78th minute as the Argentine's work for the night came to an end, and it was his goal that separated the two teams entering the final 10 minutes of the last-16 tie in Turin.
Diogo Jota came closest to netting a consolation for Porto late on, but the substitute could only find the side-netting after managing to lift the ball over the advancing Buffon.
In the end, Juventus never really needed to break sweat on the night as the Italian champions joined the likes of Barcelona, Bayern Munich and Real Madrid in the draw for the quarter-finals.