"It's never nice to concede right at the end, but the wheels keep on turning," Mihajlovic said. "I'm disappointed for the lads, they proved to themselves and others how you have to play when you wear the Sampdoria shirt."
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 goalkeeper Gianluigi Buffon was rarely troubled on his 500th Serie A appearance.
Inter is eight points behind Juventus and two behind Napoli following the surprise draw.
Bologna took the lead in the 12th minute following a swift counter attack. Jonathan Cristaldo raced down the right flank before rolling the ball across to Kone, who hadn't been picked up as he burst through the middle and sidefooted home.
Former Bologna Saphir Taider could have been sent off as he was fortunate not to receive a second yellow card in the buildup to the goal for a shirt tug on Alessandro Diamanti. The referee had played the advantage.
Inter came close to leveling on the stroke of halftime as Taider and Alvaro Pereira sent passes across goal but nobody was able to tap in. Moments later Fredy Guarin's free kick was deflected onto the crossbar.
It was back on level terms six minutes after the break when Jonathan's shot was deflected into the bottom near corner.
Bologna almost restored its lead five minutes later but Samir Handanovic pulled off a great save to deny Rolando Bianchi.
Inter nearly snatched all three points in stoppage time when Juan Jesus' volley crashed off the crossbar.
Fiorentina is two points further back, 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 counterpart 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.
