The Sunday night meeting, which somehow ended 1-0, might have been a goalfest if not for remarkable displays of goalkeeping from Gianluigi Buffon and his visiting counterpart Zeljko Brkic.
The veteran Juve stopper was particularly impressive in steering the reigning champions through a sixth league game without conceding a goal.
Brkic stood firm in the final half hour as Antonio Conte's men steadily turned the screw but Spain international Llorente burst his bubble with a header in the first minute of three added on at the Juventus Stadium.
The three points gave Juve a comfortable cushion on previous runaway leaders Roma, who were earlier held in Atalanta. The title rivals meet in the capital city on January 6.
It was a sixth straight league win for the resurgent Bianconeri while an eighth defeat of the season sees Udinese slide into 13th place.
Kevin Strootman had earlier scored on the stroke of full-time to save Roma from their first defeat of the season, but his goal was only good enough to salvage a 1-1 draw at Atalanta.
A second-half free-kick from Davide Brivio saw the Bergamo outfit threaten to end Roma's unbeaten run - the Giallorossi notched 10 straight wins before drawing three times - until Dutch midfielder Strootman spared his team-mates' blushes.
The solitary point earned from a fourth consecutive draw was only enough to see Roma draw level on points with Juve for a few hours.
With daunting games against Fiorentina, AC Milan and Catania beckoning before the two title rivals meet in Rome in the new year, Rudi Garcia's title hopefuls could pay dearly for their current slump.
In Sunday's early kick-off, Mario Balotelli helped Milan to a long-awaited league victory as they came from behind to beat Catania 3-1 at the Stadio Angelo Massimino.
The Italy striker put the Rossoneri ahead with a smart finish midway through the second half after Riccardo Montolivo had cancelled out Lucas Castro's deflected opener.
A minute after his goal Balotelli was brought down to earn Panagiotis Tachtsidis a straight red card, and Kaka wrapped up the win with a fine strike on the counter-attack.
Inter Milan were unable to impress new owner Erick Thohir with victory at San Siro as Renan scored at the death to salvage a 1-1 draw for struggling Sampdoria.
The Indonesian billionaire purchased a 70 per cent stake in the Milan giants in October and watched Fredy Guarin fire his new club ahead in the first half.
But Inter were pegged back by Samp substitute Renan, who spared his club from suffering a fourth defeat in five games with his well-taken equaliser just before full-time.
Sassuolo were denied the chance to claim back-to-back Serie A victories for the first time in their history as Cagliari rallied from two goals down to force a draw at the Stadio Sant'Elia.
The Serie B champions looked set to win again following last weekend's triumph over Atalanta when Lino Marzorati and Simone Zaza scored during the first half of action in Sardinia.
Second-half goals from Nene and Marco Sau, however, rescued a 2-2 draw for 14th-placed Cagliari.
Chievo escaped the relegation zone by comfortably beating Livorno 3-0 in Verona.
Goals from Luca Rigoni, Cyril Thereau and Alberto Paloschi decided a second straight win for Eugenio Corini's Flying Donkeys, who are now 16th, while Livorno dropped into the bottom three.