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They came close to a second through Juan Cuadrado, but Curci pushed his powerful effort around the post.
On the half-hour mark Fiorentina doubled their lead. Borja Valero received the ball just inside the box, before curling an effort into the bottom corner.
The home side continued to dominate and Giuseppe Rossi sealed the win when he latched onto a pass from Valero, before lifting the ball over the keeper and into the back of the net.