Brekalo rounded off a fine team move in the 23rd minute to put the hosts two ahead following Wilfried Singo's headed opener shortly before.
The 23-year-old made it three eight minutes later when he intercepted a dreadful pass from Jose Callejon before skipping past Pietro Terracina and slotting home.
Antonio Sanabria rounded off the scoring just before the hour mark to make it a resounding win for Torino, who move up to ninth in Italy's top flight on 28 points.
Fiorentina are four points ahead in the sixth, nine away from the Champions League positions but still well in the fight for a spot in Europe next year.
The Viola have made an impression this season, with highly-rated Dusan Vlahovic starring up front, but were comprehensively beaten on an off-night for Vincenzo Italiano's attack-minded side.
Both sides have a game in hand after their matches on Thursday were not played due to a surge in coronavirus cases across the league.
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