Elsewhere, Lazio escaped with a 1-1 draw away to ten-man Sampdoria while Fiorentina's hopes of challenging for a place in Europe next season were dented by a 1-0 defeat away to dominant Udinese.
Juventus now have a two-point cushion on overnight leaders Roma ahead of the capital side's home game against struggling Cagliari on Monday.
Napoli, stunned 1-0 at home by Parma on Saturday, are now six points off the pace in third but stayed ahead of fourth-placed Inter Milan after the Nerazzurri were held to a 1-1 draw away to Bologna.
Bologna took the lead in deserved fashion when Panagiotis Kone collected Jonathan Cristaldo's square ball on the counter and kept his cool to slot it past Samir Handanovic in the 12th minute.
Inter had a mediocre opening period but spirits were lifted six minutes after the break when an angled shot by Jonathan took a deflection off the boot of Frederik Sorensen to wrong-foot Gianluca Curci in the home goal.
Rolando Bianchi brought a great reflex save from Handanovic with a half-volley from outside the area, but from then on Inter had the lion's share of the chances and were unlucky not to claim a winner at the death.
Rodrigo Palacio's angled drive from the right was blocked and, after Fredy Guarin collected the rebound, Curci got down low to block his angled shot from close in.
In injury time Curci blocked at his near post when Rolando rose to send a bullet header goalwards from a corner.
Moments later the crossbar came to Bologna's rescue, stopping a sweetly-struck volley from Juan Jesus that would likely have become a contender for goal of the season.
Juventus travelled to Tuscany looking for their fourth successive league win, with goalkeeper Gianluigi Buffon, making his 500th Serie A appearance, having kept clean sheets in their three previous games.
Despite missing several defenders due to injury and suspension, prompting coach Antonio Conte to slot midfielder Arturo Vidal in the middle of his back three, the Bianconeri weathered a frustrating first period and made the difference in 12 second-half minutes.
Goalscoring action was scarce in a frustrating first half for both sides.
However, Juventus saw claims for a penalty waved away just before the hour despite the ball clearly coming off the arm of Federico Ceccherini.
Minutes later Llorente broke the deadlock when he smashed a volley past Francesco Bardi from Paul Pogba's cross from the right, and the Spaniard then held up several defenders to lay the ball off for Tevez to hit a low drive past the goalkeeper at his near post.
Two weeks after a 3-0 rout away to Juve, Napoli's second successive defeat also left them without influential midfielder Marek Hamsik, who suffered a foot injury, ahead of their crucial UEFA Champions League clash away to Borussia Dortmund.
Fiorentina were dominated throughout a 1-0 defeat away to Udinese that left La Viola with their third defeat of the campaign, but still in fifth place.
Sampdoria suffered a blow from the opening minute of the second half when Nenad Krsticic saw red for a challenge on Cristian Ledesma which left the Italian midfielder.
However, with new coach Sinisa Mihajlovic in charge, the hosts rallied and substitute Roberto Soriano headed Samp into a shock 67th minute lead after keeper Federico Marchetti had fumbled at the crossbar following a poor clearance.
Samp looked to have secured all three points until their defence allowed Lorik Cana to weave his way towards the edge of the area where he beat Angelo Da Costa at his near post with a low drive.