The Bianconeri battled to a 1-0 win, courtesy of a goal from Gianpiero Pinzi 24 minutes into the first half.
A bad tempered game saw nine bookings - two of which resulted in Jacopo Balestri being sent for an early bath.
The result sees Udinese climb further away from the bottom of the table, and the side will be hopeful of mounting a challenge for a top six place.
Modena - newly-promoted this season - are looking nervously over their shoulder, but will feel they can avoid relegation.
In the late Serie A game, Walter Samuel was the hero for Roma - scoring the only goal of the game against Torino.
The Argentine defender scored a goal early in the second half to give Roma the points, in a match that saw too out-of-sorts sides battle it out.
To compound Torino's misery start striker Cristiano Lucarelli failed to convert an early penalty.
Serie A:
Modena 0-1 Udinese
Torino 0-1 Roma
