The visitors created the better chances in the early stages and almost took the lead in the 24th minute when Khouma Babacar let fly from outside the box to test Francesco Benussi between the home side's sticks.
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Babacar caused Carpi all kinds of problems in the first period, and he fired Fiorentina in front 10 minutes before half time when he gained possession in the area and rifled a shot into the bottom corner.
Carpi's best chance to equalise came 10 minutes into the second half when Ryder Matos met Gaetano Letizia's cross with a header just yards from goal, but visiting goalkeeper Ciprian Tatarusanu produced an instinctive save to preserve his side's advantage.
The result leaves Carpi still without a win in the top flight, lying second from bottom in the table with one point on the board.