Livorno left 13 goal top scorer Paulinho on the bench, as they didn't want to risk a booking that would rule the forward out of next weekend's relegation clash with Chievo Verona. Innocent Emeghara was rewarded with a start after netting the equalizer against Inter Milan last week.
Emeghara forced Gianluigi Buffon into a near post save inside the first two minutes. The Swiss striker then turned provider for strike partner Luca Siligardi to shoot off target. That shocked Juve into life and the home side took over. Tevez ran between two markers to poke a shot straight at Francesco Bardi, while Giorgio Chiellini blazed over from a Paul Pogba pull-back.
Midway through the first half, Djamel Mesbah got a crucial touch to divert a Stephan Lichtsteiner effort wide, with the Swiss wingback seemingly ready to roll the ball into the net before the intervention.
The inevitable Juve goal came on 32 minutes. Llorente collected a pass from Tevez and hit a shot on the turn into the top corner. Three minutes later, the Spaniard grabbed his second when his header from an Andrea Pirlo corner squirmed underneath Bardi and crept into the net. The goalkeeper really should have done better and won't want to see too many replays. Llorente took his tally to 13 for the season.
Just before half time, Lichtsteiner was sent clear and he dragged a shot across the face of goal, while at the other end, Emeghara nutmegged Martin Caceres, only to delay his shot and allow Leonardo Bonucci to nick the ball before he could pull the trigger.
Tevez shaved the post in first half stoppage time when his curling effort flew past the outstretched hand of Bardi.
Ten minutes after the break, Pogba's disguised pass found Llorente, but the frontman ran out of space and was denied a chance at a hat-trick when the ball rolled out of play.
Just short of the hour, Buffon rolled back the years when he flew to pluck an Alfred Duncan screamer out of the top corner with a smart one handed save.
Neither side really threatened after that. Pogba should have added a third on 69 minutes. The Frenchman found space in the box, only to rush his shot and lift the ball into the stands. The game became a training ground exercise for the Bianconeri, who decided to rest their stars and conserve their energy for Thursday's Europa League match against Lyon.
Juve appealed for a penalty right at the end when Claudio Marchisio was brought down in the box. Instead, the referee showed leniency towards Livorno and blew the final whistle.
Juventus: Buffon; Caceres, Bonucci, Chiellini; Lichtsteiner, Pogba, (Padoin 84) Pirlo, Marchisio, Asamoah; Tevez, (Giovinco 66) Llorente (Vucinic 77)
Goals: Llorente 32, 35
Livorno: Bardi; Ceccherini, (Piccini 60) Valentini, Coda, Castellini; Benassi, Biagianti, (Mosquera 74) Duncan, Mesbah; Emeghara, (Belfodil 64) Siligardi