The Norwegian-born skier started the day 48 points behind Switzerland's defending champion Marco Odermatt but took the maximum 100 points from the race in Hafjell, near Lillehammer, while his rival failed to finish the first run.
Odermatt had already won the overall, downhill and super-G World Cup titles. He finished with 495 points to Pinheiro Braathen's 547.
Pinheiro Braathen, who won the slalom World Cup Crystal Globe as a Norwegian in 2023 and has raced as a Brazilian since 2024, is also challenging for the slalom title with the final race of the men's season on Wednesday.
"It’s overwhelming. I came into these finals knowing I could leave with two Globes, I could leave with zero and anything in between, and after day one, we at least got one of them," he said.
"To be able to look at this Globe with the Brazilian flag on my chest is something I’m immensely proud of.
"I may have a slalom Globe already, but the giant slalom is the basis of Alpine skiing. It’s the discipline that everyone in this sport has tried before they move on to something else."
The Brazilian was 0.21 faster than Austrian Stefan Brennsteiner in the first run, with Switzerland's Loic Meillard third.
Pinheiro Braathen was only eighth best in the second run but beat Meillard by 0.58 with Norway's Atle Lie McGrath third and Brennsteiner fourth.
Odermatt said he had taken a risk and paid the price, missing out on the chance to become the first male skier to win four World Cup globes for three years in a row.
"My plan was to take the risk, to try to attack, to try to fight for the victory, not just for some points for the globe, and it didn’t work out," he said after his last race of the season.