On a night to forget for the Giallorossi, Kevin Lasagna's early strike was compounded by a first-half straight red card for Diego Perotti - who was also captain on the night.
Substitute Illja Nestorovski then scored late on to wrap up the three points for the visitors.
Paulo Fonseca's side had some chances - the best of them perhaps coming from the lively Carles Perez - but were denied at every turn by a combination of an alert Juan Musso in goal and some resilient defending from the Udinese backline.
Fonseca's side have the chance to make amends on Sunday - they face Napoli at the Stadio San Paolo in a big game in the race for Europa League qualification.
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