Second-half goals from Fernando Llorente and Carlos Tevez proved enough to clinch the points for the champions at the Stadio Armando Picchi.
The result lifted Antonio Conte's side two points clear of Roma, who play Cagliari on Monday night, and left the Amaranto 16th in the table.
Juve had the better of the early chances, Arturo Vidal firing over and Llorente heading narrowly off target from Simone Padoin's cross, although Livorno goalkeeper Francesco Bardi was not called into action until after the half-hour mark.
He had to be on his toes to keep out Paul Pogba's drilled shot from outside the box and then again to deny Kwadwo Asamoah following a strong run and shot in the 38th minute.
Claudio Marchisio also tried his luck from distance before half-time, but his effort fizzed inches wide of the left post and the teams went in at the interval goalless.
The hosts had offered little going forward in the first period but started the second a little more brightly, Andrea Coda lashing over the bar and then Leandro Greco mis-hitting his attempt after being teed up by Andrea Luci on the counter-attack.
In the 63rd minute, however, Juve grabbed the opener, Llorente slotting home at the near post from Pogba's cross.
Tevez passed up a chance to make it 2-0 five minutes later when he arrowed a right-footed shot just wide of the far post.
But, 15 minutes from time, he did double his team's advantage. Pogba was again involved with a cross towards Llorente, who controlled the ball in the box and set up the Argentina frontman to tap home from close range.
It could have been an even more convincing margin of victory had Asamoah's bullet strike from outside the box not been punched away by Bardi, but the champions had already done enough.