The former Villarreal striker put in a man of the match performance to help the Viola to an impressive comeback win.
Antonio Conte’s side took a 2-0 lead into the break thanks to Carlos Tevez and Paul Pogba but an incredible 15-minute spell saw Fiorentina turn the match on its head as Rossi took center stage to inspire the home side's comeback.
The Italian pulled one back from the penalty spot before equalizing with a powerful finish. Joaquin gave Fiorentina the lead in the final 15 minutes and Rossi completed his hat trick late on after Juan Cuadrado's clever pass.
Vincenzo Montella's side came into the fixture having only picked up two points from its last three league matches, but he felt only one change was necessary as Facundo Roncaglia replaced Nenad Tomovic, while Fernando Llorente and Pogba replaced Fabio Quagliarella and Arturo Vidal for Juventus, the latter dropped after returning late from international duty.
Tevez and Llorente went close in a quiet opening half hour, the former heading wide while the Spaniard was denied by a Gonzalo Rodriguez intervention.
The Argentine defender would be at fault just a few minutes later, however. Tevez controlled and turned just inside the area, but was needlessly tripped by Rodriguez, allowing the former Manchester City man the chance from 12 yards, which he confidently buried.
Juve added a quick-fire second in the 40th minute. Cuadrado burst back into the area to clear the ball, but his attempt while sliding flew up into the air rather than away and gifted Pogba an easy finish from close range.
Juventus went close to opening up a three-goal lead soon after the break as Claudio Marchisio poked the ball past Roncaglia and charged into the area, but Neto blocked the midfielder’s chipped effort.
The Brazilian goalkeeper was becoming increasingly busy and was forced into two more saves before the hour mark to deny Giorgio Chiellini and Andrea Pirlo.
The second half had been dominated by the visiting side, but after Kwadwo Asamoah bundled Matias Fernandez to the ground inside the area, Rossi stroked home the resulting penalty with 24 minutes left.
Rossi pulled Fiorentina level in the 76th minute as he held off his marker and then fired across Gianluigi Buffon, into the bottom far corner, as Juve began to rue the wasted chances.
Two minutes later, Montella's side completed the turnaround and took the lead. Second-half substitute Joaquin found space in the right side of the area and calmly guided the ball past Buffon to seal a memorable comeback.
What looked like being another defeat to the Turin giant turned into an emphatic victory as Rossi completed his hat trick with nine minutes to go. He latched on to Cuadrado’s pass and fired low past the helpless Buffon, wrapping up three points.
Defeat leaves Juventus five points off Roma at the top of Serie A as the club languishes in third.