Early season pacesetters Roma had spurned the chance to regain top spot earlier when Rudi Garcia's men had to settle for their fourth draw in succession, 1-1 away to Atalanta.
Juve seized the chance to widen the gap but missed several chances before Llorente secured the points after heading Stephan Lichsteiner's shot past Zeljko Brkic in second-half injury time.
Juve's 12th win of the season - their sixth consecutively, all with clean sheets - leaves them three points clear of Roma with Napoli in third, a further six points adrift, ahead of their trip to Lazio on Monday when Fiorentina, in fifth, also host Verona.
Juve suffered an early blow when midfielder Andrea Pirlo was forced off with an apparent knock to his knee, to be replaced by Paul Pogba, but the hosts should have gone in for the half-time interval several goals to the good.
Carlos Tevez was a constant threat and tested Brkic throughout although Juve survived a scare on the half hour when defender Leonardo Bonucci lost possession to Antonio Di Natale, who saw goalkeeper Gianluigi Buffon halt his cheeky lob.
Juve's frustrations continued throughout the second half, when Buffon also had to stop strikes from Di Natale and Andrea Lazzari, but the hosts turned up the pace when Conte introduced Lichsteiner, then Fabio Quagliarella.
Swiss international Lichsteiner made his long-awaited return from injury when he replaced Simone Padoin just before the hour and with 15 minutes remaining striker Quagliarella replaced wing back Paolo De Sceglie.
Quagliarella and Llorente both came close in the final ten minutes but as the match looked to be heading for a draw Llorente reacted quickly to Lichsteiner's shot from the edge of the area to head past the wrong-footed Brkic.
Earlier, Inter Milan were stunneed by a late leveller from Brazilian Renan in a 1-1 draw at home to Sampdoria, after Fredy Guarin had given the Nerazzurri an 18th minute lead at the San Siro.
Inter remained fourth but Walter Mazzarri's men are just three points ahead of Fiorentina and now ten points behind Juventus.
Roma had Dutch midfielder Kevin Strootman to thank for a share of the points in the final moments of the match after he levelled Davide Brivio's earlier free kick as the visitors turned up the intensity in the last half hour.
Elsewhere, Chievo Verona beat Livorno 3-0 and Cagliari battled to a 2-2 draw with Sassuolo. The results send Verona out of the relegation zone and into 16th, while Cagliari remain one point ahead of Sassuolo in 14th.