Defending champions Juventus went top, at least until AS Roma host Cagliari on Monday, by winning 2-0 at Livorno with goals from Fernando Llorente and Carlos Tevez while Udinese slowed Fiorentina's progress with a 1-0 win.
The famously volatile Mihajlovic took charge of his first Sampdoria match five days after quitting his previous job with Serbia, where he had been at the helm for 18 months.
He returned to coaching in Italy almost exactly two years after leaving Fiorentina amid protests by the club's supporters which included ethnic taunts.
On a soggy pitch, lowly Sampdoria had Nenad Krsticic sent off 18 seconds into the second half for a nasty lunge at Cristian Ledesma but Lazio, without an away win all season, failed to take advantage.
The Albanian cut inside a defender and planted his shot firmly past Angelo da Costa, denying Sampdoria their third win of the season.
"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 a 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."
Llorente fired Juventus in front at Livorno with a superb volley in the 63rd minute and then laid off the ball for former Manchester City and United forward Tevez to rifle home 12 minutes later.
Fiorentina stayed fifth with 24 points when Thomas Heurtaux scored to give Udinese a 1-0 win.
Omar El Kaddouri scored twice to give Torino a 4-1 win over struggling Catania and Sassuolo continued to climb away from trouble with a 2-0 win over Atalanta.