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They came close again through Alberto Aquilani, who saw his powerful strike from the edge of the box deflect wide of the post.
In the 25th minute Fiorentina took the lead through Juan Caudrado, who picked up the ball in midfield, before working some space and firing a low shot into the bottom corner.
At the start of the second half Bruno Fernandes wasted a chance for Udinese when he drilled a shot wide of the post.
Caudrado then came close to scoring his second of the match when his powerful long-range free kick went just over the bar.
The Viola were given the chance to double their lead in the 72nd minute after Danilo gave away a penalty for bringing Cuadrado down inside the box.
Gonzalo Rodriguez stepped up and made no mistake to calmly slot the ball past Scuffet.
Rodriguez should have scored a third for Fiorentina, but after latching onto Matos's flicked header at the back post, he blazed the ball over from just a couple of yards out.
Udinese pushed for a way back into the game and scored in the 82nd minute when Fernandes's cross from the right found a way past Neto and ended up in the back of the net.
Fiorentina wasted the chance to restore their two-goal advantage just minutes later, as Cuadrado was picked out unmarked in the box, but he fired his strike against the bar.
Deep into stoppage time Thomas Heurtaux headed just wide of the post for Udinese, but Fiorentina held on to claim the three points and keep up their challenge for a third-place finish.