Charles Leclerc of Ferrari completed the podium, finishing third after a late safety car restart.
Max Verstappen received a 10-second penalty for appearing to drive into George Russell, demoting him to 10th place.
Lewis Hamilton finished seventh after being overtaken by Nico Hulkenberg, and after an earlier request to let Leclerc pass.
Piastri described the weekend as 'great overall,' praising the team for providing him with a winning car, while Norris acknowledged Piastri's superior pace.