Notching a time of 2:14.01 over the two runs, the 25-year-old finished just 0.7 seconds ahead of Austria's defending champion Marcel Hirscher, who is seeking his fourth Crystal Globe in the discipline.
Felix Neureuther of Germany was third in 2:15.38, getting on the podium for the first time at a World Cup giant slalom.
Pinturault's margin of victory was half that of Lara Gut, who won the women's giant slalom opener on Saturday
, as the result provided an early hint as to how tight this season's competition could be.
A change in the light conditions midway through the day's racing meant that the second run tended to be about five seconds slower than the first, a detail that benefited some racers, but caused others to struggle.
Switzerland's Justin Murisier, for example, was initially placed third before slipping to seventh overall following a disappointing second run.
Pinturault, however, remained undeterred, clocking the fastest time over both runs of the competition and scooping his 16th World Cup win in the process.
The 25-year-old, who has finished third in the overall World Cup standings for the past three seasons, acknowledged that the result bodes well for the rest of the campaign.
"In the beginning, you never know where you are," he told the International Ski Federation
(FIS) website. "You never know if you are skiing fast or not and just after Soelden, you can see where you are more or less.
"One thing that is easy in skiing is that there is never strategy, you just have to push and push even harder for the second run."
Pinturault, second in the giant slalom standings last season, picked up 100 World Cup points for his victory ahead of the next round of racing in Levi, Finland -- which will host the opening slalom events on November 12-13.
His rival Hirscher, who has won the previous five overall World Cup titles and is favorite to claim the giant slalom title again this time, fought back from an error midway through the final run to finish second.
"I'm super happy," the 27-year-old Austrian said. "The pressure is definitely on my shoulders, especially at the first race of the season.
"If I am skiing good, everything is fine, but if I am skiing bad, it is never fun so I am super happy and a lot of pressure has gone away."
Twenty-eight skiers qualified for the second run, with more than 50 competitors either failing to complete the course or finishing outside the time required.