With Roma's mid-season struggles continuing thanks to Saturday's 1-1 draw against Empoli, Massimiliano Allegri could have seen his side move nine points clear at the summit.
However, the holders looked jaded following their 1-0 Coppa Italia success at Parma in midweek and could have been behind at the break if Bruno Fernandes and Cyril Thereau had been more clinical with first-half efforts.
The visitors ended the half well and saw Roberto Pereyra hit the crossbar soon after the interval, but still they failed to find a breakthrough against a side whose last win at home in the league came in October.
Andrea Stramaccioni was ultimately rewarded for a solid defensive showing - having survived a late scare when Carlos Tevez shot wide - but Allegri will no doubt be frustrated after seeing his side fail to score in a top-flight game for only the third time this season.
Juve had taken 13 points from their last five league games on the road, but it was the hosts who started the brighter despite missing the suspended Panagiotis Kone and injured midfielder Emmanuel Agyemang-Badu.
Allegri was without midfield pair Arturo Vidal and Claudio Marchisio due to injury and suspension respectively, and Udinese almost made the most of their absences when Fernandes found himself clean through 12 minutes in – only to stutter and miss the chance to apply a finish.
Paul Pogba shot wide at the other end soon after, while Tevez continued to pose problems for the home side, but Udinese coped at the back and remained dangerous on the break.
Thereau was next to go close but, like Fernandes, was unable to finish a slick counter-attack midway through the half.
The unmarked Fernando Llorente headed wide from a corner and, while Juve ended the half on top, they were unable to find an opener before the change of ends.
As in the first half, Udinese began the second positively and forced Gianluigi Buffon into a smart save when Danilo flicked on Antonio Di Natale's corner.
In a fast-paced opening to the half, Pereyra rattled the crossbar with a powerful strike from inside the area before Allegri opted to replace Llorente with Alvaro Morata - matchwinner against Parma on Wednesday.
The Spaniard nearly found himself clean through on goal following a careless pass from Giovanni Pasquale, but a last-ditch challenge from Ivan Piris cleared any danger.
Morata's introduction gave Juve added impetus, with Tevez going close at the death with a close-range effort that went wide.
Ultimately the visitors had to settle for a draw that moves them back into a seven-point lead at the top, while Udinese are now winless in six at home, but will doubtless be content with their first point against Juve since 2011.
