A hard-fought match saw both sides squander good opportunities, but the hosts wrapped up the win and sealed an eighth consecutive clean sheet in the process, to move into second place in the table.
Juventus made a decent start to the match and defender Daniele Rugani came closest as he rose to meet a corner with his head, forcing a fine save from Marco Silvestri.
At the other end, Wojciech Szczesny was at full stretch to push away a deflected cross before Beto could apply a touch to score at the far post.
Moise Kean ought to have broken the deadlock for Juventus shortly before half time as he was played through by Angel Di Maria, but the striker fired straight at Silvestri to squander a glorious opportunity.
Juventus began the second half brightly, with Di Maria showing fine footwork to burst into the box and cross for Dusan Vlahovic, with his deflected flick sliced just inches over the bar by Kean.
An end-to-end encounter saw Rodrigo Becao test Szczesny from range, before Filip Kostic burst into the Udinese box and dragged a low shot just past the far post, with Silvestri beaten.
Juventus had a great chance late on when a sliced clearance saw the ball drop to Arkadiusz Milik in the six-yard box, but he could not sort his feet in time to apply the finish before Jaka Bijol hacked it away.
It would not prove costly though, as just minutes later Danilo handed the Bianconeri all three points.
Federico Chiesa brought down an excellent Leandro Paredes pass to burst into the box and volleyed across goal for Danilo to apply the finish.
Juventus remember Vialli and Castano
Before kick-off, Juventus and Udinese gathered to pay tribute to former Vecchia Signora striker Gianluca Vialli, after he tragically lost his battle against cancer on Friday.
The ex-Italy international spent four seasons at Juventus, scoring 53 goals and helping them win the Scudetto, the UEFA Cup, and the Champions League.
Gianluca Pessotto, Vialli‘s teammate at the Bianconeri, entered the pitch before kick-off to read a touching letter to his friend, whilst a minute’s silence was observed.
Juventus also took the opportunity to pay tribute to former defender Ernesto Castano, after he passed away on Thursday.
The 83-year-old had made 265 appearances for the club between 1958 and 1970, winning three league titles and four Coppa Italia trophies.