Bottas, second on the grid, got off to a slow start and was overtaken by Max Verstappen and Norris.
Bottas, whose Mercedes teammate Lewis Hamilton qualified on pole at the Hungaroring, took Norris from behind, who dethroned championship leader Verstappen.
Red Bull’s Perez, Ferrari’s Leclerc and Aston Martin’s Stroll were caught in the incident at the first corner and their cars were unable to continue, while Verstappen fell to 13th and a red flag was waved .
Norris, who fell 15th but managed to keep riding, entered the pits. His car was then abandoned by McLaren, marking the first time this season that the 21-year-old did not earn points.
Once the race resumed, all remaining drivers came to a halt except defending champion Hamilton, who was the only one making a standing start.
The Briton, who has won the race eight times and triumphed last year, fell to last place as Ocon d’Alpine took the lead, with quadruple champion Sebastian Vettel second.
Nikita Mazepin, meanwhile, was cut in the pit lane by Kimi Raikkonen and became the sixth driver to be withdrawn from the grand prix.
Hamilton quickly passed Antonio Giovinazzi, who moments later received a 10-second pit-speed stop in the middle of the restart, and even passed Vestappen’s damaged car as he climbed to fifth place.
Meanwhile, former champion Fernando Alonso passed his teammate Alpine Ocon for an unlikely and short-lived lead.
The 40-year-old fell quickly while Ocon stayed ahead, and a long battle between Alonso and a determined Hamilton ensued.
Hamilton came out on top and then beat Ferrari’s Carlos Sainz in a thrilling streak, taking third place in the process for a podium spot.
Vettel secured second place for Aston Martin, while Ocon claimed his very first F1 victory.
After the last lap Vettel told his team over the radio: “Ah man, I tried, I tried, I tried the whole race. Keeping track is so difficult. Sorry guys. “
The first round incident was the second in a row in a first round, following the crash of Verstappen in the British Grand Prix.
The Belgian-Dutch and title rival Hamilton met at Silverstone earlier this month, which resulted in Verstappen leaving the race, which Hamilton went on to win.