Defender Federico Gatti headed in a 67th-minute goal for Juventus after Dusan Vlahovic opened the scoring by earning and converting a penalty.
Kenan Yildiz sealed the result by also earning and converting a penalty in stoppage time.
Tudor was fired on Monday following three consecutive losses.
Interim coach Massimo Brambilla directed the team against Udinese, with former Napoli and Italy coach Luciano Spalletti expected to be named the club’s new manager on Thursday.
“Spalletti is a great coach, with experience and a modern style of football,” Juventus adviser Giorgio Chiellini said before kick-off.
“We have to wait, because there is no signature yet,” he added.
The victory lifted Juventus into sixth place, six points behind Italian league leaders Napoli and Roma.
AAP