The Spanish forward put the Turin giants on their way in the 32nd minute and headed home his second soon after to give Juve three valuable points in the title race.
The win preserved the Bianconeri's unbeaten home record this season and allowed them to restore their big advantage in the standings after Roma won 3-1 at Cagliari at the weekend.
The defeat has extended Livorno's winless run to four games and left them in 18th place, two points behind Bologna, who hold the last position of safety.
Juve coach Antonio Conte fielded his strongest attack with Llorente playing alongside the team's top scorer Carlos Tevez, who was returning to action after missing last weekend's 2-0 defeat at Napoli through suspension.
Livorno had the first chance to score in the second minute when Innocent Emeghara's drive from 30 yards was kept out by Juventus goalkeeper Gianluigi Buffon.
The hosts should have taken the lead in the sixth minute when Llorente set up Tevez in the box, but his right-footed shot towards the far post was saved by Livorno goalkeeper Francesco Bardi.
Livorno defended deeply and Juve controlled possession, and in the 28th minute Leonardo Bonucci wasted a chance when he struck the ball off target from a good position.
However, Juve went in front when Tevez spotted Llorente on the left side of the box and he struck the ball towards the far post and out of Bardi's reach.
The hosts then doubled their lead three minutes later when Bardi failed to punch away Andrea Pirlo's corner and Llorente was on hand to nod the ball into the back of the net.
Tevez almost made it 3-0 before half-time but his right-footed attempt from just outside the area went wide.
Early in the second half, Llorente should have had a hat-trick, but after he controlled a long ball from Paul Pogba, the Spaniard fired wide with only Bardi left to beat.
On the hour mark, Alfred Duncan's long-range attempt forced Buffon to fully stretch to clear.
Conte brought on attacking pair Sebastian Giovinco and Mirko Vucinic in place of Tevez and Llorente for the final 20 minutes, but the substitutes could not find the net despite having several chances to do so.
Juve next host Lyon on Thursday, holding a 1-0 advantage in their Europa League quarter-final tie.