Alvaro Morata struck the 83rd-minute winner for Juve two minutes after Kalinic had equalised for the hosts with a curling effort to cancel out Mario Mandzukic's first-half opener.
Juve have 85 points, 12 clear of Napoli who have four games left, and will claim a record fifth consecutive Scudetto on Monday if second-placed Napoli fail to beat AS Roma away.
Massimiliano Allegri's Juve side took one point from their opening three matches this season and were 11 points off the pace as late as Oct. 31 but they have won 24 of their 25 league games since then, picking up 73 points in that period.
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“It was nearly impossible to win 24 games out of 25," Allegri told Sky Sport Italia. "This (win at Fiorentina) was another step towards the championship."
Mandzukic opened the scoring in the 39th minute whenPaul Pogba headed Sami Khedira's lofted pass into his path.
Kalinic stunned Juve in the 81st by capitalising on an error by Leonardo Bonucci before firing past Buffon but moments later Morata levelled with a tap-in after a goalmouth scramble.
Kalinic could have rescued a point for fifth-placedFiorentina, who have 59, after earning a dubious late penalty, but his spot kick was saved by the outstanding Buffon.
“It was vital to win at a stadium where they don’t like us very much at all,” Morata told Mediaset Premium.
“(Buffon) just isn't human, he's a superhuman to save that penalty," he added. "We hope to win the title in the next round of matches."
Should Napoli beat Roma on Monday, then Juve -- the 'Old Lady' of Italian football -- will have a chance to wrap up the title when they host relegation-threatened Carpi next Sunday.
(Writing by Ed Dove; Editing by Ken Ferris)
