- Edoardo Bove (37')
- Lorenzo Pellegrini (55')
- Tammy Abraham (90'+1')
Captain Pellegrini doubled Roma's lead with a precise strike into the top left corner after being nicely teed up inside the box by striker Andrea Belotti 10 minutes into the second half.
Roma substitute Abraham wrapped up the win in stoppage time with a header.
Udinese, missing their season's top scorer Beto with flu, battled Roma for possession but lacked sharpness in attack and failed to create any real danger in front of Patricio's goal.
Jose Mourinho's Roma side will look to recover from a goal down in their Europa League quarterfinal when they host Feyenoord in the second leg on Thursday before travelling to Atalanta in Serie A on April 24.
Udinese are 12th on 39 points and host second-bottom Cremonese next Sunday.
- Antonio Giua