The Gialloblu arrived as giant-killers having beaten AC Milan on the opening day of the Serie A season but reigning champions Juve failed to heed the warning and conceded an opportunistic goal from Fabrizio Cacciatore.
Carlos Tevez responded emphatically with a fiercely-struck equaliser and Llorente, making his bow at the Juventus Stadium, completed the turnaround with a header deep into first-half stoppage time.
The victory offered reason to be cheerful to Juventus after a disappointing week which saw the Bianconeri held to 1-1 draws by both Inter Milan and FC Copenhagen, while Verona could take heart from a plucky performance that enhanced their reputation as the newcomers mostly likely to prosper.
Perhaps in a defiant response to reports he had been dissatisfied with Llorente's pre-season performances following his free transfer from Athletic Bilbao, Juve coach Antonio Conte handed the Spaniard a first start of the new season.
For most of the first half, though, it looked like he would be upstaged by fellow summer signing Tevez, as the dynamic Argentinian relentlessly terrorised the Verona box.
He tried his luck from distance before Leonardo Bonucci fed Llorente in the area, Rafael rushing out to block.
After Hellas enjoyed a good chance through Daniele Cacia, Tevez steamed up the other end to rifle a fierce strike at Rafael. The Brazilian received a cut to his chin in the tussle that followed and play was briefly suspended.
The Brazilian keeper was back on his feet to deny Paul Pogba a free header and, on 25 minutes, he watched Tevez twist and drive an effort just over his crossbar.
Tevez came knocking once again after exchanging swift passes with Arturo Vidal but after Rafael made the save, Verona raced up the other end to score.
With the Juve backline distracted, Vangelis Moras' header snuck through to Cacciatore in the six-yard box and he tucked home without any fuss.
The Bianconeri response was immediate and clinical as Tevez waited just two minutes to seize on Bonucci's through-ball and rocket a shot just under the bar.
Verona were reeling and, three minutes into time added on, Llorente opened his account for the Italian champions with a headed finish from Vidal's cross.
The visitors put their heads together over the break and came out strongly, Jorginho quickly finding himself in a shooting position, where he was denied by Bonucci.
Juve pushed back and had Rafael sprawling to parry an Andrea Pirlo free-kick in the 64th minute.
The bar saved Verona moments later, though, as Pogba's shot on the turn caught the keeper unawares.
But try as they might, the Bianconeri could not find a third goal to finish their opponents off but Sebastian Giovinco - a late substitute for Tevez - looked particularly dangerous around the box to keep Rafael sweating until the very end.