Serie A: Juventus 2 Livorno 0
With third-placed Napoli losing to Parma on Sunday, Juve coach Antonio Conte knew three points against their relegation-threatened visitors on Monday would seal UEFA Champions League football next season.
And the reigning champions, who are now eight points clear of Roma in second and 20 in front of Napoli with just six games remaining, put in an assured display with Llorente, who sat out the midweek UEFA Europa League win at Lyon, striking twice in three first-half minutes.
The Spaniard's first was an emphatic finish from inside the six-yard box, and he then saw a near-post header creep under Francesco Bardi to ensure Juve bounced back from just their second league defeat of the season at Napoli last week by maintaining their perfect home record in Serie A this term.
The second half lacked the intensity of the first, with neither side really coming close to scoring, as Juve seemed content to control proceedings by dominating possession.
Livorno, meanwhile, stay two points adrift of safety in 18th place.
After threatening through Innocent Emeghara in the opening minute, the visitors struggled to contain Conte's side and their goal led a charmed life.
Giorgio Chiellini and Stephan Lichtsteiner wasted early chances for the hosts, but Juve’s pressure eventually paid dividends with Llorente’s quickfire double just after the half-hour mark.
Carlos Tevez was the architect for the opener, as he played a neat pass into Llorente, before the Spaniard spun away from his marker and lashed the ball into the top corner.
The 29-year-old then doubled his tally with a close-range header. Andrea Pirlo delivered a corner to the near post and Llorente's header somehow squirmed under Bardi.
Paul Pogba and Tevez both had opportunities to extend Juve's lead further in the closing minutes of the half, but their long-range efforts were just wide of goal.
The start of the second half mirrored the first as Livorno came out very quickly, but their inability to test Gianluigi Buffon meant the hosts were able to keep them at bay.
Juve were far from their best after the break and looked to hit their opponents on the counter-attack, although chances were at a premium.
Llorente's search for a hat-trick saw his first sight of goal in the second half hit the side-netting, while Pogba scuffed an opportunity wide from inside the area.
Livorno's Alfred Duncan finally called Buffon into action just before the hour, and the Italy keeper was equal to his long-range effort with a one-handed save.
With Thursday's Europe League quarter-final second leg with Lyon on the horizon, Conte was able to rest Pogba, Llorente and Tevez in the final 20 minutes of the match as Juve took another step towards their third consecutive Scudetto.