More than 90 fans were arrested before the match after Partizan's team bus was pelted with rocks when approaching the stadium and rival supporters also fought running battles on Belgrade's outskirts, Serbian police said in a statement.
"The incidents, including a few minor scuffles, resulted in the arrest of 92 individuals, three of whom were juveniles," it said.
In the stadium, Red Star fans burned several seats at the final whistle after both sections of supporters had lit dozens of flares and unleashed firecrackers early in the second half, forcing referee Milorad Mazic to halt play while the billowing smoke cleared.
The result left Partizan five points clear of Red Star at the top of the table with two rounds remaining and firmly on course to win a record sixth successive league title after substitute Jojic curled in a delightful 90th-minute free kick.
It also ended Ricardo Sa Pinto's perfect eight-game winning streak after the former Portugal forward took over at Red Star in March and hauled the 1991 European Cup winners back into the title race from an 11-point deficit.
"It was difficult to lose like this after winning eight in a row and getting into a position to leapfrog Partizan and we were also unlucky with some of the referee's decisions," Sa Pinto told a news conference.
"We had some chances in the first half but our game up front fell apart after (striker) Darko Lazovic limped off with an ankle injury early on."
His counterpart Vuk Rasovic was delighted after his maiden derby, having been appointed coach last month.
"It was the ideal outcome of a difficult match in which we defended well to weather the early storm and then controlled the game to earn this priceless win," he said.
"I congratulate the players for this memorable moment and I am sure the celebrations will last until the early morning hours."