The 2011 champion, Grange reclaimed the title with a daring go-for-broke second run in limited visibility down a deteriorating Birds of Prey track to post a two-run winning time of one minute, 57.47 seconds.
Germany grabbed the other two spots on the podium with Fritz Dopfer finishing 0.35 seconds adrift to take silver and World Cup slalom leader Felix Neureuther the bronze.
"Skiing, it's always hard, but it's easier when you are on the podium and when you win," said Grange, who had not set foot on a World Cup podium since a third-place finish in 2011. "I was out of the podium for four years so I can't expect this. It's a dream.
"The big events, like world championships and Olympic Games, there is always a lot of press and a lot of pressure and you are not always feeling good, but you have to believe in yourself.
"Today was my day."
Fifth after the opening run, a daunting 0.88 seconds back of Hirscher, the 30-year-old Frenchman posted the best second-leg time of the day, 53.21 seconds, and then stood in the finish area and watched as the final four medal contenders failed to push him from top spot.
Hirscher, looking to give Austria a sixth gold medal that would match their best performance at a world championships, held a slim lead as he came in sight of the finish area, only to lose control and straddle a gate.
"I didn't expect that," said Grange, adding he had considered retiring after injuries and a string of poor results. "This year I just wanted to go for a medal.
"I had my first podium here and then I had a bad injury in the knee but it was in giant slalom.
"I have a lot of emotion in Beaver Creek, bad and very good."
It was only the third time in 11 events that Austria failed to land a skier on the podium.
Austria finished the two-week championships atop the medal standings with five golds, three silvers and a bronze. The United States claimed victories in the men's giant slalom and women's slalom on the final weekend to jump into second with two golds, one silver and two bronzes.
(Editing by Gene Cherry)
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