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The defeat for Inter means that they have now shipped seven goals in their last two Serie A games, and it was Khouma Babacar who opened the scoring for La Viola after seven minutes.
Mauro Icardi almost drew his side level when he curled a shot wide on the edge of the area, and moments later, Fiorentina extended their advantage.
The Colombia international almost claimed his second of the evening after the restart, but Handanovic did well to close the angle as the midfielder got his shot away.
Nenad Tomovic made it 3-0 with just under a quarter of an hour left when he finished off a move with an effort at the near post.