Gut, who led after the first run, finished with a total time of 2min 25.16sec, ahead of Austria's Kathrin Zettel at 2:26.00 and Germany's Viktoria Rebensburg at 2:26.44.
"It's the first race of the season and already a win, it's amazing," Gut said.
"I'm happy to bring a giant slalom win to Switzerland again," she said.
The 22-year-old's best result in the World Cup giant slalom so far had been third places in Semmering in 2008 and in Lenzerheide in March.
Her three World Cup wins had been in the speed disciplines, in the downhill and super-G.
"The last years I was used to skiing fast but I was also used to making a lot of mistakes," Gut said.
"In training this summer we really practiced skiing clean and this is what I did in the first run, just try to ski clean and push to the limit," she said.
"I didn't like the first run, the snow was pretty aggressive and there was a big distance between the gates.
"I like it when there are more turns and it's hard, it's riskier," Gut said.
"So I was confident that the second run would be different," she said.
"I just tried to ski fast.
"It's an incredibly cool course, the first time I was here (in 2008) we had sensational conditions, I really had fun but the next few years were difficult," she said.
"Now I have a good relationship again with this slope."
Gut's nearest rival Zettel, who came second here last year, took her fifth podium in Sölden, where she won in 2008.
Rebensburg won here two years later.
Zettel has struggled with injury over the past few years but felt she was back at her best.
"I'm more relaxed — I had a good summer," she said.
"The last years have been getting better from year to year and this year I felt really good."
For Olympic champion Rebensburg, a podium place was not even a goal
"It's a tough course, tough snow and pretty steep," she said.
"And it's the first race of the season so nobody knows where they stand," said the 24-year-old.
"I didn't really have any expectation of a result, I just wanted to ski good and to have fun."
The overwhelming favourite to win on Saturday, giant slalom and overall World Cup winner Tina Maze of Slovenia, produced a rare poor performance, finishing 18th, 3.05 seconds behind Gut.
Maze won here last year and had been chasing a record fourth win in Sölden.
On the other hand, young US star Mikaela Shiffrin — who broke through last season, winning the slalom crystal globe and world championship title — impressed with two smooth runs, to finish sixth.
US star Lindsey Vonn, Maze's biggest rival, decided to sit out the first race following a knee injury suffered in a bad fall at the world championships in February.