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The hosts started the encounter the better of the two sides as Andrea Poli shot over the Viola crossbar in the opening minutes.
However, Fiorentina soon began to assert themselves on the game and went ahead in the 36th minute when Juan Cuadrado fired home from 30 yards.
Alberto Aquilani ended the game as a contest in the 73rd minute when he scored his side's third goal of the afternoon, turning home Ljajic's free kick from just yards out.
Sampdoria ended the match with 10 men after Daniele Gastaldello was shown a straight red card seven minutes later for a bad challenge on Ljajic.