Substitute Stephan Lichtsteiner, making his return from two months on the sidelines, saw his shot diverted in by Llorente to secure a 1-0 win in the third minute of added time on Sunday – Juventus' sixth league triumph in succession.
Second-placed Roma also had a late intervention, in the form of Kevin Strootman's close-range finish, to thank for preserving their unbeaten record at Atalanta.
The hosts led when Morgan de Sanctis misjudged Davide Brivio's 51st-minute free-kick and Roma are now without a win in four games, their runaway early-season form an increasingly distant memory.
Milan put boardroom upheaval to one side as they came back from a goal down to defeat 10-man Catania 3-1.
Lucas Castros' 13th-minute strike took a deflection of Daniele Bonera to open the scoring, but Riccardo Montolivo levelled matters with a fine volleyed finish from Urby Emanuelson's cross.
Mario Balotelli crashed a low free-kick through the Catania wall and into the bottom corner and was then on the receiving end of the high tackle that saw Panagiotis Tachtsidis dismissed before an excellent angled effort from Kaka completed the scoring eight minutes from time.
Milan manager Massimiliano Allegri and his Catania counterpart Luigi De Canio played down a flashpoint between Balotelli and home defender Nicolas Spolli after the match, following reports that the Italy striker reacted angrily to alleged racial abuse from the Argentine before being substituted.
Fourth-place Inter could not welcome new president Erick Thohir with a win over Sampdoria, with the match at the San Siro another to produce late drama.
Fredy Guarin gave the hosts a 17th-minute lead after Ricky Alvarez bamboozled Sampdoria defender Andrea Costa, but a superb 25-yard drive from substitute Renan ensured a share of the spoils with a minute remaining.
Cagliari fought back from 2-0 down to claim a 2-2 draw against fellow strugglers Sassuolo.
Ex-Milan defender Lino Marzoratti powered home a header and Simone Zaza doubled the advantage, but Nene and Marco Sau were on target inside the last 15 minutes for the home side.
Chievo's upturn in fortunes under Eugenio Corini continued, with Luca Rigoni, Cyril Thereau and Alberto Paloschi on target in the 3-0 win over Livorno.
