Juve, who have now lost just one of their last 21 meetings with city rivals Torino, climb level on points with Napoli at the top of the Italian top flight.
There was a good chance for Juan Cuadrado to open the scoring six minutes in, but he sent the ball over the bar at the end of his slaloming run.
Dybala opened his account for the evening with a rasping drive from the edge of the area soon after, and matters got worse for the visitors when Daniele Baselli was dismissed for a high challenge on Pjanic.
Salvatore Sirigu was needed to keep out Pjanic, though he was to be beaten for a second time prior to the break as the Bosnian midfielder swept home Cuadrado's cross into the top corner.
Moments after sending a shot inches wide, Sandro went one better 57 minutes in when getting ahead of his marker to head home from a Pjanic corner.
Torino, unbeaten in the league prior to tonight, were struggling to live with their opponents and shipped a fourth before the full-time whistle sounded.
Dybala was the man who bagged it, scoring for the 10th time in seven outings by getting the better of Sirigu with a deft flick in added time.