Vučić had spent two terms as president and could not seek a third term, so was leading his Serbian Progressive Party (SNS) with the aim of returning to the post of prime minister, which he left in 2017.
The Student List's lead candidate Ilija Srdanović told BBC Serbian: "This will be a free state."
He said the anti-corruption movement, which had attracted anti-government voters across Serbia, hoped to "free the country from tyranny".
There were celebrations on the streets of the city, with people dancing and chanting "victory", cars honking, and fireworks set off. "Serbia is free," one student told the BBC. "It's a miracle."
During a celebration speech, Student List candidate Radomir Saicic said Serbians had shown "no obstacle was greater than their will", Reuters reported.…