Germany's Kira Weidle-Winkelmann and Emma Aicher took the silver, 0.05 behind, and Jacqueline Wiles and Paula Moltzan finished third for the United States after the decisive run down a slalom piste set by Austrian coach Robert Berger.
World and Olympic downhill champion Johnson and dominant slalom skier Shiffrin, the overall World Cup leader, had looked set to repeat their 2025 world championship win but finished fourth - the most painful position for any Olympic athlete.
"We didn't really expect it," said Huber, of her feelings after Shiffrin left the start hut as the last skier down.
"For me, it was true, (I thought) Mikaela would do it. That was really, really a surprise in the end, a gold medal for us."
Johnson was fastest in the downhill to put Shiffrin, who has won seven out of eight slaloms this season and is also the most successful World Cup skier of all time, in the driving seat.
The skier who would have been a safe bet to bring home the gold suddenly took on a different character, finding herself off the pace with the advantage evaporating in the sunshine of Cortina d'Ampezzo's Olimpia delle Tofane piste.
Her slalom run was only the 15th fastest, an unheard-of result for someone who has beaten most of her rivals by more than a second over two legs this season.
The sense of deja vu was palpable - Shiffrin, a three-time Olympic medallist from 2014 and 2018, arrived at the 2022 Beijing Games as favourite to win a fistful of medals but left empty-handed. She has two more chances in the giant slalom and slalom.
"I didn't quite find a comfort level that allows me to produce full speed," said the American, who added that the "feeling under the feet" was not there on softer snow than experienced this season.
"So I'm going to have to learn what to do, what to adjust in the short time we have before the other tech races. There's always something to learn."
The fourth place ended Johnson's hopes of a 'double double' - holding both the world downhill and team combined titles and adding Olympic golds in both.
Silver was Swedish-born all-rounder Aicher's second of the Games after she finished runner-up in the downhill. Remarkably, the German skied the slalom leg on Tuesday and was also the fastest on the slope, 0.03 quicker than Switzerland's Wendy Holdener.
Huber was 10th , but Raedler had set up the gold by coming second in the downhill.
"Katharina, she really kept it together in the end," said Austrian Alpine skiing director Christian Mitter of a skier who won team gold in Beijing. The current format of the best technical and speed skiers paired together is being used for the first time at the Games.
"We couldn't count on gold, but you never do... They were good runs, Olympic performances," added Mitter.