Fiorentina registered the first threat of the game when Josip Ilicic had an effort comfortably saved before Antonio Di Natale, who has netted 10 goals this season, saw a long-range strike tipped wide by Neto.
The visitors were having the better of the action at Stadio Artemio Franchi, and they almost took the lead when Di Natale headed against the post from a Emmanuel Badu delivery.
That near miss sparked Fiorentina into life with Ilicic and Babacar both having shots saved by Orestis Karnezis, and although Udinese frustrated their hosts for the remainder of the half, they couldn't get to the break without conceding the lead to the home outfit.
After the ball had made its way into the Udinese penalty area, Babacar was in the right place at the right time to fire the ball home from close range for his third goal of the season.
The second half began with Fiorentina still on top and Babacar leading the line well in attack as the Senegalese forward was given the ball on the edge of the area before seeing a shot kept out by Karnezis.
Jose Basanta squandered an headed opportunity midway through the half, but five minutes later, Fiorentina deservedly doubled their lead when Babacar got on the end of a Juan Cuadrado pass to convert into the roof of the net.
Ten minutes from time, the result was put beyond doubt when Cuadrado set up Valero to fire into the bottom corner from 20 yards to seal the three points for his side.