Goalkeeper Zeljko Brkic kept Udinese in the lead, while his counterpart Neto also made a number of saves.
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 their previous three matches and their hopes of ending that run took a blow when Krsticic was shown a second yellow card at the start of the second half.
However, they 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 when Lorik Cana drilled into the bottom-left corner.
Catania are now level with bottom club AC 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 Domenico Berardi against fellow strugglers Atalanta.