The pair had started the day at Brazil's Interlagos circuit separated by a single point, with Norris on pole position and closest rival Piastri third on the grid.
The Australian's hopes disappeared on lap six of 24 when he lost control on the wet kerb at turn three and spun into the barriers.
The race was then halted on lap eight, resuming with a rolling start after barrier repairs and Norris leading the field with Mercedes's Kimi Antonelli and George Russell in his slipstream.
The race ended with double yellow flags waved after Sauber's home hero Gabriel Bortoleto crashed heavily, with Antonelli having to settle for second, 0.845 seconds behind Norris. Russell took third place.
Red Bull's reigning world champion Max Verstappen finished fourth and is now 39 points behind Norris in third place overall.