The Norwegian-born Brazilian beat Switzerland's Loic Meillard by a combined 0.54 of a second in Kranjska Gora, with Austrian Stefan Brennsteiner third.
Odermatt, the World Cup overall leader who is also top of the standings in downhill, super-G and giant slalom, finished fifth.
That left the Swiss 48 points clear in the GS standings with one race, worth 100 points, still to come at the World Cup finals in Norway on March 24.
Odermatt has a massive 632-point lead over technical specialist Braathen in the overall World Cup, with eight races remaining across all disciplines.
Braathen was 0.14 quicker than Brennsteiner in the first run and fourth equal in a second run where the pace was set by Norway's Atle Lie McGrath, who ended up fourth.
It was Braathen's second win of the season and first in a giant, apart from the Milano Cortina Olympics.
"I'm just skiing with a lot of happiness, a lot of joy," he said of a win that came two years to the day since he announced his comeback under the Brazilian flag after leaving the Norwegian team.
"The only thing I've been trying to do since the Olympics is enjoy it, whilst obviously trying to combine that with getting ready for some difficult last races and a lot on the line, fighting for various titles.
"Just not trying to make too big a deal out of it: ski with the flow, ski with my heart."
Braathen is also a contender for the slalom title and is one point behind leader McGrath.
The men have a slalom in Kranjska Gora on Sunday.
