The on-loan Juventus striker struck three times in 19 first-half minutes – the first coming from the penalty spot and the third following a defensive mistake from Gonzalo Rodriguez - as Sassuolo raced into a 3-0 lead on Tuesday to boost the club's hopes of a great escape.
Rodriguez made partial amends for his wayward pass when he pulled one back from the penalty spot before Nicola Sansone restored Sassuolo's three-goal advantage with 25 minutes remaining.
There was still time for Giuseppe Rossi to net his first goal since returning from a cruciate knee ligament injury sustained in January before Juan Guillermo Cuadrado further reduced the deficit for Fiorentina, bidding to bounce back after defeat against Napoli in the Coppa Italia final on Saturday.
But Sassuolo withstood late pressure that included Borja Valero having a looping 94th-minute header disallowed for offside as the visitors clinched a vital three points in the scrap for survival.
Victory lifts Sassuolo above Bologna and Chievo with two games remaining.
Defeat for Fiorentina ensured Napoli clinched third place and UEFA Champions League play-off qualification before Rafael Benitez's men defeated 10-man Cagliari 3-0 in Tuesday's other game.
Dries Mertens broke the deadlock from the penalty spot after 33 minutes. Flanked by two defenders, Goran Pandev attempted to twist and turn away before being hacked down and Mertens tucked the resulting spot-kick hard and low past the outstretched Marco Silvestri, who guessed the right way.
Pandev doubled his side's lead with his first league goal of 2014 two minutes before the break.
Silvestri conceded a penalty and saw red nine minutes after the restart when he fouled Pandev just before the hour mark, but Marek Hamsik crashed his effort against the crossbar.
It mattered little, however, as Blerim Dzemaili added a third minutes later after Vlada Avramov could only parry Pandev's initial effort.
