Serie A: Milan 0 Juventus 2
After spending most of the first period on the back foot, Juve pounced in the final minutes of the half through Llorente's close-range strike before Tevez scored spectacularly from distance after the break to confirm a win that moves Antonio Conte's men 11 points clear of Roma.
The result also continues Juve's remarkable run of scoring in every league game this season as goals from both strikers kept them on course for the title.
A home reverse ended Milan's bid for a third straight league victory but they will certainly take heart from their first-half performance in particular, when they could have scored but for a combination of wasteful finishing, a goal-line clearance and the presence of Gianluigi Buffon in the Juve goal.
Milan were without Mario Balotelli through injury but created early openings when Adel Taarabt fired in a long-range effort that Buffon easily dealt with, before Kaka blasted wide.
Tevez and Llorente were back in the starting XI after being rested for the UEFA Europa League clash with Trabzonspor and they combined well to fashion an early chance for the visitors, but Tevez shot straight at Christian Abbiati.
The champions should have taken the lead after 18 minutes when Stephan Lichtsteiner met a low cross at the back post, only for Abbiati to produce a fine save.
In a breathless opening, Milan went close to breaking the deadlock after 25 minutes when Kaka saw his first effort saved by Buffon and, although he beat the Italian with the rebound, Leonardo Bonucci cleared off the line.
Milan continued to impress and Andrea Poli wasted a good chance after 32 minutes when he sliced over from 18 yards.
Buffon had to be at his best a few moments later as he made a sprawling save to palm away Riccardo Montolivo's piledriver.
Juve were under siege and Kaka produced a fine curling effort that forced Buffon into a superb save. Poli should have converted the rebound but fired over.
And the hosts were made to pay for their profligacy a minute later when Lichtsteiner pulled the ball back for Llorente to tap home his 13th of the season
The pace showed no signs of dropping early in the second half.
Tevez brushed Adil Rami off the ball before forcing Abbiati into a low save before, at the other end, Taarabt's cross was missed by everybody and Buffon had to parry the ball away.
Juve made the game safe after 67 minutes when Tevez produced a stunning 25-yard strike that flew past Abbiati and went in off the crossbar.
The scoreline could have been even worse for Milan soon afterwards, as Andrea Pirlo and Paul Pogba both hit the woodwork late on, but a third would have been harsh on Milan - who struck the frame of the goal themselves in a frantic finish through Robinho.