The result, which takes Juventus to second in the top flight, means that Massimiliano Allegri's side are now just a point behind leaders Napoli.
Bologna failed to make a telling impact on the game, and were solid defensively until Pjanic opened the scoring. Juventus, however, pressed further and were rewarded with a solid victory.
The opening chance for Juventus came when Sandro played Pjanic in at the edge of the 18-yard box, but the midfielder's shot failed to test Antonio Mirante in the Bologna goal.
The away side went in front after 27 minutes when Ibrahima Mbaye's sloppy tug on Sandro gifted Pjanic the opportunity to tuck away a free kick, which was taken when the Bosnian's effort went in off the hand of Mirante, who had stepped away from his near post.
Allegri's side were two up 10 minutes later when Pjanic's well-weighted ball over the top of Mbaye was chested down by striker Mario Mandzukic, whose shot across Mirante's goal had enough power to beat the Italian.
Juventus began the second half looking to secure the win as another dangerous ball from Sandro was sliced out of play by Filip Helander.
The third goal was supplied by Blaise Matuidi after 65 minutes, whose first strike for the club came when Helander's clearance was drilled past Mirante on the half-volley.