Ferrari’s Charles Leclerc came third as Piastri stretched his lead in the drivers’ standings over Norris to 16 points.
Heavy rain delayed the 13th round of the season by 80 minutes, with organisers eventually allowing a rolling start after four laps behind the safety car as the sun finally appeared.
Pole sitter Norris was quickly passed by Piastri as Norris complained he had a problem with his car’s battery.
Piastri then produced a controlled race from the front to lead home McLaren’s sixth 1-2 of the season.
“I knew lap one was going to be my best chance of winning the race,” said Piastri. “Rest of race we managed really well.”
“Oscar did a good job, nothing more to say,” said Norris.
Max Verstappen, winner of Saturday’s sprint, took fourth in Laurent Mekies’ first race weekend as Red Bull team principal after the sacking of Christian Horner a fortnight ago. (AFP)