Diminutive forward Sebastian Giovinco scored twice against his former club and Hernan Crespo and Raffaele Palladino also found the net for Parma at Turin's Stadio Olimpico.
It was a negative day for Juventus from the start, with forward Fabio Quagliarella exiting with an apparent knee injury just three minutes in. Then in the 17th, Felipe Melo kicked Parma defender Massimo Paci in the face and was sent off.
The 1.64-meter (5-foot-5) Giovinco, who was used mostly as a reserve by Juve the past two seasons, pounded in a rebound from close range in the 41st and doubled the lead from the edge of the area in the 48th.
Nicola Legrottaglie pulled one back for Juve with a header in the 60th but Crespo was then fouled by Giorgio Chiellini inside the area in the 61st and converted the ensuing penalty. Palladino added another in injury time before Juventus was whistled off the pitch.
Juventus remained fourth, five points behind leader AC Milan. Parma moved up from 16th to 10th.
"This is a huge victory, against a squad that is fighting to win the title," Crespo said.
