Red Bull's Max Verstappen finished second in a race that ended in the rain at Interlagos and teammate Isack Hadjar was third. George Russell was fourth for Mercedes and Kimi Antonelli fifth in his first race since becoming world champion.
Norris took the chequered flag, waved by Brazilian footballer Neymar, 14.602 seconds clear of Verstappen.
"It was a very tough race. Very, very tough," said Norris, the 2025 world champion, of his 14th career win and 50th podium as well as his team's first victory since August.
"A lot of challenges today with the conditions and going onto slicks in the wet is always tough, especially when you are pushing for the lead and trying to catch up a little bit," added the Briton, who lost out to Antonelli at the start.
"The main thing today was I kept it cool and didn't make any mistakes and had the pace when I needed to. Nice to be back on the top step and what a place to do it as well."
Mercedes had needed to score only three points more than Ferrari to clinch the title, and the Italian team never threatened to prolong the fight, with Charles Leclerc seventh and Lewis Hamilton ninth.
The title was Mercedes' first constructors' crown since 2021 and came a week after 20-year-old Italian Kimi Antonelli became the youngest drivers' champion with four races to spare in Mexico City.
"It was a very strong beginning of the season and that kind of got us over the line. These last few races have been challenging at times, today it was difficult, but overall I'm so proud for the organisation," said team boss Toto Wolff.
McLaren's Oscar Piastri was sixth with Racing Bulls' Liam Lawson sandwiched between the Ferrari drivers in eighth after a fine race that saw the New Zealander start third and run in second place for the first five laps.
Nico Hulkenberg took the final point for Audi in a race of spins, slippery moments and changeable conditions.