The hosts would have been relatively confident having only lost two of their previous 26 league matches at the Stadio Artemio Franchi, but Antonio Conte’s side took a 2-0 lead into the break thanks to Carlos Tevez and Paul Pogba.
However, a spell of 15 minutes saw Fiorentina turn the match on its head as Rossi took centre-stage to inspire the hosts' comeback.
The Italian pulled one back from the penalty spot before equalising 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 their 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.
The visitors 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 visitors, but after Kwadwo Asamoah bundled Matias Fernandez to the ground inside the area, Rossi stroked home the resulting penalty with 24 minutes left.
Italy striker 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 their 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 giants turned into an emphatic victory as Rossi completed his hat-trick with nine minutes to go as he latched on to Cuadrado’s pass and fired low past the helpless Buffon, wrapping up the three points.
Defeat leaves Juventus five points off Roma at the top of Serie A as they languish in third.
