Second-placed AS Roma had brought the title race to life by slashing Juve's lead from 14 to five points in the previous eight days but Monday's comfortable win left Antonio Conte's side eight points clear with six matches to play.
Juventus, who have 84 points from 32 games, also have the easier run-in with matches against midtable Udinese, Atalanta and Cagliari and relegation-threatened Bologna and Sassuolo as well as a visit to Roma in the penultimate round of the season.
Roma must still face Fiorentina and AC Milan and finish with a tough match at Genoa.
The visitors defended bravely for half an hour, occasionally threatening themselves, before Llorente opened the scoring with a superb strike in the 32nd minute, firing home on the turn.
The Spaniard struck again three minutes later, taking his tally to 13 in his debut Serie A season, with a glancing header which goalkeeper Francesco Bardi appeared to have covered but then allowed to slip through his hands.
Juventus, who are still in the Europa League, relaxed in the second half, often playing the ball around between the back three to eat up time.
Livorno stayed in the relegation zone in 18th place with 25 points, two adrift of safety.
- Sports & Recreation
- Antonio Conte