The forward duo struck in the first half as Antonio Conte's side took another step toward retaining their Serie A crown.
A run of seven straight league victories has brought Roma back into title contention and, with Udinese unbeaten at the Stadio Communale Friuli since January, the scene was set for a potential upset Monday.
However, Antonio Conte's men put in an assured performance and with just five games remaining it appears more a question of when rather than if Juventus will claim a third consecutive league title.
Sebastian Giovinco - making just his fourth league start this season - got the ball rolling in the 16th minute and Juve led by two at the break when Fernando Llorente grabbed his 14th top-flight goal of the campaign from close range.
Juventus failed to match its first-half standards after the interval, choosing instead to slow the pace of the game, though Giovinco almost had a second when he saw a shot rebound off the post.
With Carlos Tevez only among the substitutes because of a thigh problem, Giovinco was afforded a rare starting berth and he duly delivered the opener.
The forward collected the ball on the right-hand side of the box before skipping past Maurizio Domizzi and curling past Simone Scuffet with his left foot.
Giovinco then forced Scuffet into a near-post save and Juve doubled their lead from the resulting corner after 26 minutes.
Andrea Pirlo's delivery was flicked toward the back post by Claudio Marchisio and, after a bout of pinball in the area, Llorente provided the simple tap in from six yards.
Udinese enjoyed a spell of possession at the end of the half, but Juve dealt with the threat well, Giorgio Chiellini making one particularly fine interception from Antonio Di Natale's pass to deny Dusan Basta a run at goal.
The second half was played at a slow tempo, as Juventus were happy to sit back and maintain possession. Giovinco was still proving a lively threat, though, and a quick turn of pace from the 27-year-old in the 66th minute led to him breaking into the box but his cross narrowly evaded the head of Llorente.
The Italy international was again in the thick of the action for Juve's next chance, showing good feet in the box before shooting against the post.
Substitute Luis Muriel also struck the woodwork at the other end, but Juve recorded its 18th clean sheet in the league this season, meaning it could seal the title before traveling to Roma on May 9.