The Olympic super-G champion's risk-taking paid off as she finished ahead of two Austrians with Cornelia Huetter at 0.12sec and Mirjam Puchner 0.13 off the pace.
With Shiffrin still recovering from a knee injury, Gut-Behrami now leads her rival by 305 points in the overall standings to close in on the World Cup title she previously won in 2016.
"I never expected to be still racing at 32 and to be so consistent," said Gut-Behrami.
"I'm looking forward to the next races and keep on skiing well."
Shiffrin should return to competition next weekend in the Swedish resort of Are, where a giant and a slalom are planned, before the finals in Saalbach, Austria, from March 16 to 23.
Gut-Behrami will not take part in the slaloms, which leaves hope for Shiffrin, who has the opportunity to take 200 points from her in this event before the end of the season.
Gut-Behrami claimed her eighth success this season, the best record of her career, and a 45th victory in the World Cup.
She has the second-best record of active skiers behind Shiffrin, men and women combined.
"I'm trying to enjoy the good feeling I have," said the Swiss skier.
"I know I don't have many years left on the circuit."
On Saturday, a downhill race had initially been scheduled but due to adverse weather conditions, training sessions planned for Thursday and Friday could not take place and the event was transformed into a super-G.
A second super-G is scheduled for Sunday in the Norwegian resort.
To conquer a fifth small globe in the super-G, Gut-Behrami is still battling with Huetter and Italian Federica Brignone, who was sixth on Saturday.
