Norris' teammate and title rival Oscar Piastri picked up a penalty for causing a collision and finished fifth.
Mercedes' Kimi Antonelli hung on for a career-best second place with Red Bull's Max Verstappen third after starting from the pitlane, another astonishing performance from the four-time world champion who won from 17th on the grid last year.
Australian Piastri, who started fourth at Interlagos with sprint winner Norris on pole, had to serve a 10-second penalty for an early clash with Antonelli that put Ferrari's Charles Leclerc out of the race.
George Russell was fourth for Mercedes, who consolidated second place overall in a constructors' championship already won by McLaren.
The two Ferrari's failed to finish after being involved in crashes.
A Racing Bull's team strategy finally worked out for Lawson who only made one pit stop and managed to nurse home a set of medium tyres.
Lawson, who started seventh on the grid, started on softs, but they were soon ineffective and he was forced into the pits.
While his team-mate Isack Hadjar made a second pit stop to change to a set of soft tyres late in the race, Lawson stayed out and completed 50 laps on a worn set of mediums to grab seventh place, just ahead of Hadjar.
The result, his third best this season, moves the 23-year-old Kiwi up to 14th in the standings.
There are three rounds remaining in Las Vegas, Qatar and Abu Dhabi.
- Reuters / Additional reporting on Liam Lawson from RNZ
