Tevez, Llorente hand Juve win
Tomas Heurtaux scored for Udinese, which had lost four of its past five matches.
Sampdoria played the entire second half with 10 men after Nenad Krsticic was sent off.
Also, teenage forward Domenico Berardi struck again as Sassuolo beat Atalanta 2-0 while Torino crushed Catania 4-1.
Juventus faced something of a crisis in defense, with Stephan Lichtsteiner and Andrea Barzagli injured and Angelo Ogbonna and Leonardo Bonucci out suspended. Mauricio Isla, Sebastian Giovinco and Simone Pepe were also out with injury.
The visitors broke the deadlock shortly after the hour mark when Llorente volleyed Paul Pogba's cross into the top corner with a magnificent strike.
Llorente turned provider in the 75th to set up Tevez for a low drive into the bottom corner.
Andrea Coda almost scored an own goal to extend Juventus' lead when his diving header hit the post from Simone Padoin's cross.
Juventus goalkeepr Gianluigi Buffon was rarely troubled on his 500th Serie A appearance.
Fiorentina is 10 points behind Juventus, in fifth spot, after losing at the Stadio Friuli despite dominating for much of the match.
Udinese scored the only goal of the game against the run of play when Roberto Pereyra nodded on Antonio Di Natale's free kick for Heurtaux to volley home at the far post in the 34th minute.
Goalkeeper Zeljko Brkic kept Udinese in the lead while his opposite number Neto also made a number of saves.
Udinese moved into the top half of the table and is a point behind eighth-placed Lazio.
It was Mihajlovic's first match in charge since taking over at Sampdoria after failing to guide Serbia to the World Cup. Mihajlovic played for both Lazio and Sampdoria.
Sampdoria had lost its past three matches and its hopes of ending that run took a blow when Krsticic was shown a second yellow card at the start of the second half.
However, it took the lead in the 67th minute. Lazio goalkeeper Federico Marchetti did brilliantly to parry Manolo Gabbiadini's effort, before scrambling up to swat away another shot, but Roberto Soriano headed in the rebound.
Lazio leveled at the end when Lorik Cana drilled into the bottom left corner.
Catania is now a point behind Sampdoria and level with bottom club Chievo Verona after a hefty defeat in Turin.
Sebastian Leto got Catania back into the game at the start of the second half following goals from Ciro Immobile and Omar El Kaddouri. But Emiliano Moretti and El Kaddouri sealed the match with two in as many minutes.
Sassuolo moved three points above the relegation zone with goals from Simone Zaza and Berardi against fellow strugglers Atalanta.