The match was played under tight security after diehard Red Star fans hurled a flare at Stojkovic on the team bus when Serbia were in Genoa on October 12 for a Euro 2012 qualifier against Italy.
The qualifier was abandoned after six minutes of play after rioting Serbia supporters threw flares at home fans and players.
Since joining Partizan on loan from Sporting Lisbon in August, Stojkovic has been targeted by Red Star fans who have printed fake obituaries of the keeper and displayed insulting banners during their team's home games.
Greeted by a chorus of jeers from Red Star fans on Saturday when he came out of the tunnel, Stojkovic drew a standing ovation from the Partizan faithful when he revealed a defiant message on a shirt under his jersey.
"Forgive me for my ugly past," read a slogan displayed to Partizan fans after the match in which he barely had to make a save after the champions stifled out their bitter city foes.
"My position on Red Star has changed after the Genoa incident and I was eager to show their fans today that nothing will destroy me," Stojkovic told reporters.
"I am a Partizan player now, that's where my future is and I am not afraid of hooligans."
The win sent Partizan top of the 16-team first division ahead of Red Star on goal difference, with both clubs collecting 22 points from nine matches.
