The defending champion looked on course for a comfortable evening when Mario Mandzukic netted after two minutes, but Parma made life difficult for its esteemed guests until the former Croatia international intervened again to tee up Blaise Matuidi's winner.
Gervinho had drawn Parma level on his full debut and the hosts could have led at the interval, before their momentum waned after the restart.
There was still no breakthrough for Juve new boy Cristiano Ronaldo as his barren start to life in Italy continues beyond an international break, during which he will miss action for Portugal.
The visitors made a rapid start, with Mandzukic meeting Juan Cuadrado's pinpoint cross and then beating the recovering Simone Iacoponi to the loose ball to stab into the net.
That sensational start suggested a Juve romp was on the cards, but Leo Stulac's swirling free-kick soon crashed against the crossbar and a Parma equaliser came before the break.
Gervinho was on hand to turn the ball over the line after Roberto Inglese's header, from an enticing Massimo Gobbi delivery, evaded Wojciech Szczesny, who at least prevented Luca Rigoni from completing a first-half turnaround.
But a moment of real quality saw Juve reclaim its lead and ultimately win the match just before the hour-mark as Mandzukic flicked into Matuidi's path and the France international provided a superb finish from a tight angle.
Juventus hosts Sassuolo after the international break, with its UEFA Champions League bid starting in Valencia days later. The season gets no easier for Parma, which will head to Inter Milan next.