The 24-year-old trailed favourites Alexis Pinturault and Marcel Hirscher after the first run but carved his way down the rutted course in spectacular style to win by 0.20 seconds.
Olympic champion Hirscher had to settle for the silver medal as Austria's wait for a gold at the Are championships continued.
Pinturault, who set the pace after the first run to raise hopes of becoming the first Frenchman to win the coveted GS title since Jean-Claude Killy in 1968, came third as he clocked only the 19th quickest second run.
Kristoffersen had not won a giant slam race since 2015 and was second at last year's Winter Olympics behind Hirscher.
The slalom specialist picked the perfect moment to end that wait with a dynamic run but still had to wait anxiously in the finish with Hirscher and Pinturault still to ski.
"We've been working so hard, with my dad and the team, everyone's been working insanely," Kristoffersen said after claiming his first world championship medal.
"This is amazing. I've not won a GS since 2015."
Mild temperatures meant soft snow conditions but the leading three produced a thrilling battle for the fans.
Pinturault, who won the combined title in Are, had earned a 0.10 advantage after great rival Hirscher after the opening run and it appeared to be a straight duel between the two of them for the gold medal.
But Kristoffersen had other ideas as he added his name to a long list of Norwegian world champions with an attacking run straight out of the now-retired Aksel Lund-Svindal's textbook.
American Ted Ligerty, bidding for a record-extending fourth giant slalom world title, could not find the desired speed and finished down in eighth spot.
(Writing by Martyn Herman; Editing by Toby Davis)
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