Max Allegri's Bianconeri got the job done at Estádio do Dragão thanks to quick-fire second-half goals from substitutes Marko Pjaca and Dani Alves.
Juventus were calm and patient throughout and it paid dividends on 72 minutes when Pjaca, who had replaced Cuadrado, score his first goal for the Italian giants.
Paulo Dybala's attempted through ball deflected nicely into the path of the young Croatian who needed no second invitation to fire beyond Iker Casillas.
Within 145 seconds, Juventus were two to the good when Alves smartly controlled with his chest a curling cross from Alex Sandro before hitting a lovely half-volley with his left foot.
From there it was all academic for Juve who will take a handy two-goal lead back to Turin for the return bout on March 14.
2016/17 UEFA Champions League - Round of 16 first leg
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