The Nerazzurri had to do without Walter Samuel, Ivan Cordoba, Esteban Cambiasso and Cristian Chivu.
The home side took the lead only after a couple of minutes when Simone Pepe went one-on-one with the keeper to slide past him.
But Mario Balotelli restored parity four minutes later with a well-placed shot from outside the area.
Maicon put Inter ahead on 21 minutes after volleying home from close range.
Diego Milito gave the visitors a two-goal advantage with a precise header on the stroke of halftime.
Antonio Di Natale pulled one back for Udinese upon converting a penalty kick eight minutes from the hour mark.
Defending champions Inter are now leading the league table with 58 points, four ahead of closest rivals AC Milan, who beat Atalanta 3-1 on the same day.
The match's goals