The Red Bull driver, starting from pole position with Norris alongside, finished 0.395 seconds clear of Mercedes' George Russell, with Carlos Sainz third for Williams and Lewis Hamilton fourth for Ferrari.
The eight points for victory left Verstappen 55 adrift of championship leader Piastri with the main grand prix to come on Sunday and five further rounds after that, including two more sprints.
The 19-lap race finished behind the safety car after Aston Martin's Lance Stroll and Haas's Esteban Ocon collided three laps from the end.