The pair had started the day at Brazil's Interlagos circuit separated by just a single point, with Briton Norris on pole position and closest rival Piastri third on the grid.
Norris was leading before the action on Saturday was suspended on lap seven of 24 after Piastri hit the barriers at turn three.
Norris navigated his way through the chaos to lead every lap and take the chequered flag just eighth tenths clear of Mercedes' Kimi Antonelli.
The win allows him Norris to extend his title lead over 24-year-old Melburnian Piastri from one point to nine.
Max Verstappen is now 40 points adrift of Norris with 108 points on the table.
Norris was in control of the action before Piastri dramatically hit the barriers at the start of the sixth lap. Franco Colapinto and Nico Hulkenberg also collided with the wall in the same part of a damp Interlagos track, leading to a safety car, and then a red flag.
Piastri dipped his front-left tyre on to the kerb on the exit of the Senna Esses which sent him into a spin and an unavoidable date with the wall.
The golden rules to tackling a damp track - following an overnight storm in Sao Paulo - are to avoid white lines and taking too much kerb and Piastri failed to adhere to the latter.
The abused tyre barrier on the exit of turn three required repairs and the race was red-flagged.
Piastri had held a 34-point lead at the summit of the standings following his win in the Netherlands on the final day of August.
But the Australian's campaign has unravelled since and his latest error comes after he crashed in qualifying in Azerbaijan in September and then on the first lap of the race in Baku, before he caused a pile-up in last month's sprint race in Austin which led to both him and team-mate Norris failing to finish.
Back to Interlagos and a 24-minute delay followed the suspension before a rolling start allowed Norris to avoid the perils of a standing start. Norris saw off Antonelli's interest before going on to win.
"It was tough," said Norris. "It makes the win look rewarding when you have a race like this. Kimi did not make my life easy. It was sketchy. It was not an easy race but the sort of race you would expect here in Brazil."
Lewis Hamilton started only 11th and took three drivers prior to the first corner to settle into eighth and then improved one position following Piastri's demise to take seventh.
