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After the break Fiorentina took control of the game and scored their third of the afternoon in the 63rd minute. Aquilani saw his header from David Pizarro's cross saved by Rafael, with Valero on hand to tap home the rebound.
Verona's hopes of getting back into the game took a blow six minutes later, when Marco Donadel was sent off for bringing down Cuadrado, with the Fiorentina man clean through on goal.
Despite being a man down, the hosts pulled a goal back in the 73rd minute. Pizarro brought down Iturbe inside the box and Luca Toni stepped up to convert from the spot.
Ten minutes later Fiorentina were awarded a penalty of their own after Domenico Maietta had handled the ball inside his own area.
Alessandro Matri took the resulting spot kick and placed the ball into the bottom corner, with the keeper diving the wrong way.
The visitors quickly added a fifth goal three minutes later, as Aquilani tapped home from close range after Cuadrado's shot had been spilled by Rafael.
In stoppage time Iturbe pulled another goal back for the home side with a powerful strike from the edge of the box, but it proved little more than a consolation as Fiorentina held on to claim the three points.