The two have been close rivals in recent times, sharing 13 wins between them in the last 16 races in the discipline.
But on Sunday it was Hirscher who came out on top, with Pinturault failing to make the podium at all.
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The Frenchman had in fact held the edge by 0.09seconds after the first run but he struggled on the second and fell back to fourth position.
Austrian Hirscher meanwhile kept his cool to finish with a combined time of 2:39.95 to take the win ahead of Sweden's Matts Olsson, 1.50 seconds back, and Germany's Stefan Luitz in third.
In picking up the win, Hirscher becomes the second man to reach 20 World Cup wins in two different disciplines, a feat achieved only by Ingemar Stenmark so far - his 20th slalom win achieved last week.
He tops the overall standings on 1260 points with Henrik Kristoffersen the nearest competition on 828 points while, with two giant slalom races to go this season, he holds a 97-point advantage over Pinturault who is chasing his first giant slalom globe.