Brignone, the 2020 overall champion who came fourth and fifth in the two downhills this weekend, pushed her run to the limit, taking risks as she flew down the mountain, very nearly missing a gate.
The 34-year-old, who was wearing bib number six, recovered her balance to clock 1 minute 30.11 seconds, finishing 0.06 seconds ahead of her Swiss rival.
"I'm a bit lucky today with the hundredths, but it was hard to make a perfect run," said Brignone.
"I made these mistakes and I thought it was possible to do better than what I did, and actually it was in some sections," she said.
"But nobody did a perfect run, and mine was better than the others."
Gut-Behrami, who followed her, began poorly before hurtling down the latter part of the course and almost sneaking victory on the line.
"I'm not really happy with the way I skied, I made a lot of mistakes in the middle part," said Gut-Behrami.
"I thought it was pretty slow in the middle. I had no chance to stay on course, I was always too late, so I was definitely surprised (to finish second)."
"It's something I've been doing the entire season, so I'm working on that, trying to change that, because my skiing is fast, but I'm always making too many mistakes."
A second Italian Sofia Goggia was a heartbeat slower, finishing 0.09 seconds behind Brignone who secured her second super-G victory and her eighth in all disciplines this season.
In the overall World Cup standings, Brignone now has a 251-point lead over Gut-Behrami, with nine races (100 points per race) to go before the end of the season.
"This is the best time of my life because I can do it also in the races," she said.
"I'm really confident about my skiing. When I'm on skis I can do what I want, and this is why it's been an amazing season for me.
"Making fourth and fifth in both downhills was already a good result, but with the victory today, it's the cherry on the cake."
Gut-Behrami still leads the super-G standings with a 55-point advantage over Brignone.
"I'm trying to do my best, and if possible win a few more races," said the Swiss.