The Bianconeri dominated the game and could have gone ahead as early as the second minute had Arturo Vidal's shot not been off target.
Mirko Vucinic then came close to scoring for the Turin giants in the 18th minute with a close-range header.
Antonio Conte's side were awarded a penalty in the 33rd minute after Antonio Mirante was adjudged to have fouled Stephan Lichtsteiner inside the 18-yard box.
However, Vidal failed to capitalise on that, as he saw his spot kick saved by Mirante.
Juve continued to call the shots, with Vidal, Vucinic and Sebastian Giovinco testing Mirante in the Parma goal before the end of the first half.
The Old Lady made a positive start to the second half and eventually broke the deadlock.
Kwadwo Asamoah's cross was brilliantly met by Lichtsteiner, who shot home from close range in the 54th minute.
Four minutes later Juventus doubled their advantage, as this time Andrea Pirlo found the target with a stunning free kick.
The defending Italian champions could have added to their tally had Giovinco scored from one of his number of chances, but ultimately had to settle for a 2-0 victory.