Behrami had already won the overall, giant slalom and super-G titles and was bidding to become only the fourth woman to take four globes in a season, a feat previously achieved by Americans Mikaela Shiffrin and Lindsey Vonn and Slovenia's Tina Maze.
Hutter, who had been third overall and 72 points adrift of the Swiss going into the race, tore up the script with a lightning run down the Ulli Maier piste to win in one minute 45.08 seconds from 12th on the starting list.
Gut-Behrami, starting 14th, was 1.89 seconds slower and ended up only 16th, losing out by 28 points with Italian Sofia Goggia third in the final standings despite being absent due to injury.
Slovenia's Ilka Stuhec finished second in the race, 0.17 slower than Hutter, with Italy's Nicol Delago third and 0.49 off the pace in warm conditions.
Slovenia's Ilka Stuhec finished second in the race, 0.17 slower than Hutter, with Italy's Nicol Delago third and 0.49 off the pace as later runners challenged in warm and windy conditions.
There were two delays to the race and Stuhec, the fourth last to start, almost snatched victory from Huetter with the Slovenian clocking a quicker time at the final intermediate but then drifting wide.
Delago was one hundredth of a second faster than Austrian early leader Christina Ager.
"I'm really speechless," said Hutter. "It's amazing to have a home race with this ending, I never can imagine it.
"I slept so bad and I woke up and I thought 'Give your best, it's the last chance today for this season' and I did it."
Gut-Behrami could still take comfort in the achievement of being the first Swiss female skier since Vreni Schneider in 1995 to win three different globes in a single season.
"In the end I'm really happy about the season... I can't really complain," said the Swiss, whose path to the overall title was helped by American Mikaela Shiffrin missing 11 races after a downhill crash in January.
Goggia had led the downhill standings, 149 points clear of Gut-Behrami, when she suffered a season-ending break to the tibia in her right leg in February.
Shiffrin secured the slalom title for an eighth time before the World Cup finals.
The downhill win was only the second of Huetter's World Cup career and the crystal globe was her first.
The race was also a farewell to Norway's retiring Ragnhild Mowinckel, the 2018 Olympic downhill silver medallist. She finished 20th and last.
