A deflected strike from man-of-the-match Juan Cuadrado midway through the first half and a second half penalty from Gonzalo Rodriguez put Fiorentina ahead before a late strike from Bruno Fernandes reduced arrears.
The game started brightly as Luis Muriel burst into the Fiorentina area only to be denied by a well timed challenge and Ryder Matos wasted a free header from a promising position for the Viola.
Simone Scuffet showed his natural instincts when he pushed a close range Matos header behind as the majority of efforts were off target in the game. Fiorentina dominated possession as the visitors were happy to sit back and hit them on the break.
Eventually the pressure would tell as Cuadrado fired in a low effort from outside the area and courtesy of a deflection off Danilo it bounced awkwardly into the far corner past Scuffet to give Fiorentina a merited lead.
Vincenzo Montella’s side looked comfortable in possession and threatened from almost every set piece as Udinese seemed incapable of competing aerially with the Viola.
After half time it was the visitors who threatened with Bruno Fernandes guiding his effort across the face of goal from a difficult angle and immediately after at the other end Scuffet had to parry a rasping effort from Cuadrado.
Cuadrado came close again to doubling his tally for the day as a Thomas Heurtaux back pass nearly came within reach of the Colombian but Scuffet managed to scramble the ball clear just in time.
The game was fast becoming all about Cuadrado as the forward was now at the heart of everything for the Viola and he had yet another effort at goal, albeit an ambitious free kick from forty yards that flew only inches over the crossbar and had the keeper clutching air.
On 70 minutes Matos played in Cuadrado who was bundled over in the penalty area and the resulting spot kick was calmly dispatched by Gonzalo Rodriguez.
Rodriguez wasted a fantastic chance as he could only fire his far post effort from close range high over the bar following yet another headed knock down in the visitors area.
Udinese would get back in the game thanks to a fantastic effort from Fernandes who shot ambitiously from out wide and caught Neto off guard to give Udinese hope.
Fiorentina rallied and moments later they were inches from restoring their two goal lead as Cuadrado was in the right place to fire in another effort only to be denied by the crossbar as the game entered the final five minutes.
Silvan Widmer came close to snatching a dramatic equaliser in injury time but his effort flashed past the post and confirmed defeat for Udinese.
The win has increased Fiorentina’s grip on finishing in fourth place as they now hold a five point advantage over fifth placed Inter whereas Udinese remain in fourteenth place in Serie A.