The win sent them eight points clear of AS Roma at the top on 87 points with five games remaining as a scudetto that has rarely looked in doubt heads towards the dominant Turin side.
Italy's Giovinco opened the scoring with a sweet curling strike after 16 minutes and fellow World Cup hopeful Llorente of Spain tapped in his 14th of the season following a goalmouth scramble at a corner 10 minutes later.
"This was a potentially dangerous match and we could not afford to drop points," Juve coach Antonio Conte told reporters.
"The title race is still open and we did well to face this match with the right determination, approach and concentration."
Without top goalscorer Carlos Tevez, it was left to Giovinco to provide Juve with thrust up front and his second of the season was a signal to Italy boss Cesare Prandelli that he was not to be forgotten.
Cutting in from the right, he whipped in a superb shot with his left that flew past rookie Udinese keeper Simone Scuffet, who was unsighted by four players.
Tiny Giovinco was unlucky in the 69th minute when managing to squeeze off a shot after impressive close control in the area only to see his effort rebound back off the post.
"I'd been looking for that goal, as I'd not scored for a while. I'm glad it came in a match as important as this," said man of the match Giovinco.
Llorente's stabbed finish from close range, which game after Scuffet poked the ball away from Paul Pogba as it pinged around the area, was less elegant but ended the match as a contest.
"It was a decisive match. We're very happy because there are fewer games left and the points difference is the same so it went brilliantly well for us," Llorente said.
Juve were comfortable enough to substitute their match winners with Mirko Vucinic and Pablo Osvaldo to see out victory before Luis Muriel hit the post for Udinese in stoppage time.
Udinese stay 14th on 38 points after a flat performance befitting a side that has all but mathematically secured Serie A safety and has little left to play for.
Francesco Guidolin's side are 13 points clear of the drop zone and were playing two years to the day since the tragic death of their player Piermario Morosini, who died after suffering a heart attack and collapsing on the pitch while playing on loan at Livorno.
Juve have to travel to the Italian capital to face Roma, who beat Atalanta 3-1 on Saturday, in their penultimate match next month but the title could already be sewn up by then.
Conte's charges have only lost twice all season in Serie A and have won all 16 of their home games. They next face relegation-threatened Bologna and Sassuolo either side of their Europa League semi-final first leg at Benfica.
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- Antonio Conte