Oliveira is also the first Portuguese rider to win a Grand Prix race in the premier class.
Several Grands Prix were cancelled or postponed after the aborted opening round in Qatar, prompting the Fédération Internationale de Motocyclisme to draft a new calendar.
The race was named for Styria, the state of Austria that the Red Bull Ring is located in.
The first practice session ended with Jack Miller fastest for Pramac Racing ahead of Ducati's Andrea Dovizioso and Tech3's Miguel Oliveira.
On the opening lap, Joan Mir got a fantastic launch from P3 to the lead the race from polesitter Pol Espargaro, with Miller also getting a great start from fourth on the grid.
After running wide and gaining an advantage at Turn 1 on the opening lap Mir was forced to drop a position, thus Miller inherited the race lead.
Championship leader Fabio Quartararo made a poor start, and dropped to P14 after running wide at Turn 1.
Takaaki Nakagami got past Pol Espargaro and the top three slowly pulling clear of the chasing pack.
Miller was leading Mir fought back on the exit but the Ducati rider held the inside line for Turn 6, with Nakagami dropping to seventh.
The top five were close, however Mir and Dovizioso were about to drop off the pace slightly with Doviziosio running wide again at Turn 9.