Despite dominating the early exchanges, the hosts fell behind in the 36th minute as Fabrizio Cacciatore knocked home from close range, but that goal served as a motivator for the champions.
Carlos Tevez, who had squandered an earlier chance, equalised in style five minutes before the break and then Llorente nodded in right at the end of the first period.
That proved to be enough to give Juve the points after draws against Inter and Copenhagen in the last week.
Following their UEFA Champions League exploits in Copenhagen on Tuesday, coach Antonio Conte shook things up by making five changes.
Marco Storari, Andrea Barzagli, Mauricio Isla, Kwadwo Asamoah and Llorente all came into the starting XI, replacing Gianluigi Buffon, Stephan Lichtsteiner, Giorgio Chiellini, Federico Peluso and Fabio Quagliarella.
Verona came into the game off the back of a 2-0 victory over Sassuolo, with three changes from that side as Domenico Maietta, Raphael Martinho and Juan Ignacio Gomez had their respective places taken by Alejandro Gonzalez, Matteo Bianchetti and Massimo Donati.
Juventus were in the ascendency from early on against the Serie A new boys, but they struggled to create clear-cut chances during the first half hour.
Tevez wasted a good chance 30 minutes in, and it was not long before Hellas made them pay for their profligacy as they capitalised from a corner when Cacciatore tapped in from close range.
Tevez made amends before the break, however. Leonardo Bonucci played an impressive throughball into the right side of the area, and the Argentinian fired a shot past Rafael into the far corner.
He almost added another too when he hit the post from distance, but Conte’s side did go into the break ahead as Llorente headed in Arturo Vidal’s cross from the right on the stroke of half-time.
The visitors started the second half positively and Jorginho had a chance to equalise, only for the excellent Bonucci to poke the ball away with a last-ditch tackle.
Juventus did not test Rafael again until just before the hour mark when Paul Pogba twice tried his luck from distance, and although the goalkeeper almost made a mess of both efforts, he was not beaten.
Frenchman Pogba seemed determined to score and he once again went for goal from outside of the area in the 66th minute, but his curling effort flew just over the crossbar.
Conte's side continued to press for late goals, but Verona remained solid at the back - although a late comeback never appeared likely.
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