Italy's Stefano Gross was third.
Kristoffersen, who leads Hirscher by 140 points, is third in the overall World Cup standings, behind Austria's Hirscher and fellow Norwegian Aksel Lund Svindal.
Svindal won the downhill at Wengen while Kjetil Jansrud won the combined, making it a Norwegian clean sweep.
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Next stop for the men is Kitzbuhel, starting on Tuesday, where a super-G, a combined a downhill and slalom are planned.
In a women's giant slalom in Flachau, Germany's Viktoria Rebensburg topped the podium for the first time this season.
(Writing by Martyn Herman, editing by Pritha Sarkar)
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