Mauro Camoranesi cancelled out Andrea Dossena's opener, but Vincenzo Iaquinta scored the winner with his first touch.
"This comeback is worth so much because the team was able to react after a first half under pressure," said Ranieri. "After the break we took control of the tempo and dominated. I must compliment Udinese, a team built very well who play great football.
"He did well to score straight after stepping on to the field. The real problems for a Coach are when you don't have the players to take off the bench. I am satisfied with the return of Camoranesi, Jonathan Zebina, Giorgio Chiellini and Gigi Buffon."