The Bianconeri got the three points following an own goal from home goalkeeper Maduka Okoye and Nicolo Savona's strike, with the ball bouncing off the right post immediately before both goals.
It was only Juve's second win in six matches in all competitions and lifted them up to third, ahead of the rest of the weekend's fixtures.
They are four points behind Serie A leaders Napoli, who host fourth-placed Atalanta on Sunday.
Udinese remained seventh and could be leapfrogged by AC Milan if the Rossoneri win at Monza later.
Only two points separated Udinese and Juventus coming into the match.
Juventus took the lead in the 20th minute with a wonderful piece of play from Khephren Thuram, who burst into the box and nutmegged a defender before taking a shot from a tight angle. The ball bounced off the inside of the far right post and in off the back of Okoye.
It would have been a first goal in Italy for Thuram, the younger brother of Inter Milan's Marcus Thuram.
Udinese had a number of chances to level before Juventus doubled their lead in the 37th.
The same post had a part to play again as Kenan Yildiz's finish was deflected off almost exactly the same spot and Savona fired in the rebound.
Udinese thought they had got back into the match early in the second half but Keinan Davis' effort was ruled out immediately as he had pushed Juventus defender Federico Gatti, causing him to crash into goalkeeper Michele Di Gregorio.
Udinese slipped to eighth after they were leapfrogged by AC Milan, who won 1-0 at Monza.
Bologna welcomed back club captain Lewis Ferguson 203 days after his anterior cruciate ligament injury and the midfielder helped the team to its first home victory since even before he was sidelined.
There was a standing ovation when Ferguson was brought on in the 82nd minute and again when he first touched the ball moments later.
And Ferguson was involved in the only goal of the match to help Bologna beat Lecce 1-0 and get their first home win in seven months. He spread the play down the left, where the cross came in for Riccardo Orsolini's header into the far bottom corner with five minutes remaining.
Ferguson, who was key to Bologna's impressive campaign last season, needed surgery after injuring his knee playing against Monza on April 13, ruling the Scotland midfielder also out of the European Championship.
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