Torino forward Andrea Belotti missed a penalty for the third time this season but then scored a brace for the visitors in the second half after Riccardo Saponara and Nikola Kalinic had given the hosts a two-goal halftime lead.
It was all too familiar for Fiorentina fans who last Thursday watched their team go 2-0 up at home to Borussia Moenchengladbach -- and 3-0 on aggregate -- in the Europa League but then collapse to a 4-2 defeat.
Some 300 fans protested at a training session on Sunday, demanding the resignation of coach Paulo Sousa, but the Portuguese said he would not stand down.
The result left Fiorentina eighth in Serie A, increasingly out of touch with the race for Europa League places, with Torino one place behind them.
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"I will sleep well tonight because I've done my job with great honesty," Sousa told reporters. “The fans pay for their tickets, they have every right to make their feelings known. “They’re the soul of the club, they’ve been here the longest.”
Saponara gave Fiorentina an eighth-minute lead, turning in the rebound after Torino goalkeeper Joe Hart superbly stopped Borja Valero's shot, and Kalinic headed in seven minutes before the break.
Torino were nowhere to be seen and only Hart prevented a bigger lead for Fiorentina.
The second half was a completely different story and Fiorentina survived a let-off when Belotti sent a penalty against the crossbar after Carlos Salcedo had tripped Lucas Boye, the fifth out of nine spot kicks squandered by the Bulls this season.
Fiorentina's relief was short-lived, however, as Belotti headed a goal back in the 65th minute after being left completely unmarked.
The home fans could sense what was coming and five minutes from the end Daniele Baselli's cross found Belotti who slotted home his 19th goal of the season, making him joint top scorer alongside Gonzalo Higuain of Juventus and AS Roma's Edin Dzeko.
"We weren't on the pitch for the first hour," said Torino coach Sinisa Mihajlovic, whose side have won only one out of nine games since the New Year.
"We prepared for the match in a certain way and did exactly the opposite on the pitch. All five (missed) penalties were decisive and if we had converted them, we could have six or seven more points."
(Writing by Brian Homewood in Berne; Editing by Clare Fallon)
