Juve have 34 points from 13 games, two more than Roma, after recording their fifth successive league win without conceding a goal.
Napoli, beaten 1-0 by Parma on Saturday, are third on 28 while Inter Milan are fourth, a further two points behind, after drawing 1-1 at Bologna.
Llorente fired Juve in front with a superb volley in the 63rd minute and then laid the ball off for former Manchester City and Manchester United forward Tevez to rifle home 12 minutes later.
The volatile Mihajlovic took charge of his first Sampdoria match five days after quitting following 18 months in charge of Serbia.
He returned to coaching in Italy almost exactly two years after leaving Fiorentina amid protests by the club's supporters that included ethnic taunts.
On a soggy pitch, third from bottom Sampdoria had Nenad Krsticic sent off 18 seconds into the second half for a nasty lunge on Cristian Ledesma but eighth-placed Lazio, without an away win all season, failed to take advantage.
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Roberto Soriano scrambled the ball in for the hosts in the 67th minute and they were on the point of celebrating their third win of the season when Lorik Cana broke clear four minutes into stoppage time.
The Albanian cut inside a defender and planted his shot firmly past Angelo da Costa.
"The lads showed how to play and how to battle with the Sampdoria shirt," said Mihajlovic. "We played well and aggressively, we didn't stop attacking even with one man less and we always tried for the win.
"A lack of attention cost us dearly but we played well, gave everything and deserved the win."
Inter fell behind to an early goal at lowly Bologna when Panagiotis Kone broke clear to sidefoot the ball home in the 12th minute.
The visitors created a flurry of chances, with Fredy Guarin hitting the bar and Rodrigo Palacio missing two excellent openings, before full back Jonathan levelled with a deflected shot six minutes after the break.
Fiorentina stayed fifth on 24 points after Thomas Heurtaux's 34th-minute goal gave Udinese a 1-0 win.
Omar El Kaddouri netted twice as Torino beat struggling Catania 4-1 and Sassuolo continued to climb away from trouble with a 2-0 win over Atalanta.
(Reporting by Brian Homewood in Berne, editing by Tony Jimenez)
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