Mihajlovic's position on the Bologna bench had been under discussion ahead of the visit of their Roman opponents after three matches without a win which included shipping six goals at Inter Milan and last weekend's miserable defeat to Empoli.
However two quick early goals from Musa Barrow and Arthur Theate gave the hosts an advantage that Lazio, who were without star striker Ciro Immobile, could not overcome.
Scotland's Aaron Hickey sealed the three points in the 68th minute when he cut inside Manuel Lazzari and let off a low shot which squirmed under Pepe Reina.
"I knew we would put in a good performance today, because if we go out there with the right attitude, we can win games," Mihajlovic told Sky Sport Italia.
Bologna moved up to ninth on 11 points, level with Atalanta, Lazio and Juventus.
Francesco Acerbi compounded an awful performance from Maurizio Sarri's side with 14 minutes remaining when he was sent off for first committing a foul on Roberto Soriano and then arguing with the referee.
Later on Sunday Napoli defend their 100 percent record at high-flying Fiorentina, Roma host Empoli trying to bounce back from last week's derby defeat, and AC Milan travel to Atalanta in the late match.
