The result left Partizan four points clear of Red Star in the two-team title race with two games left. Partizan can win the title on Thursday when they visit third-placed OFK Belgrade.
With the head-to-head record decisive if two teams finish level on points, two from their last two games would be enough for Partizan because they also beat Red Star in the reverse fixture.
Partizan dominated proceedings and were twice denied in the first half by excellent saves from Red Star goalkeeper Sasa Stamenkovic
Although Red Star held their own in the second half, they were undone by a superb 73rd-minute goal from Petrovic.
The Serbia midfielder received a pass in Red Star's half and curled an unstoppable shot into Stamenkovic's top left corner from 25 metres, leaving the goalkeeper clutching air.
Partizan's faithful lit dozens of flares and hurled them on to the running track, but the derby - played under tight security as it has a history of serious crowd trouble - was otherwise incident-free before and during the encounter.
"It was lively game of football and both teams conducted themselves with dignity and a sense of fair play, which is especially important given the importance of the match," Partizan coach Aleksandar Stanojevic told reporters.
