The medal was a first in a major event for Johnson, who returned last December from a 14-month ban for three anti-doping whereabouts failures and has had a career punctuated by injury.
Austria's Mirjam Puchner took silver on home snow and Czech Ester Ledecka the bronze.
Johnson completed her run in one minute 41.29 seconds and watched a string of rivals fail to match the time before she could celebrate becoming the first American downhill world champion since Lindsey Vonn at Val d'Isere in 2009.
Vonn, the 2010 Olympic champion making a championships comeback at the age of 40 after retiring in 2019, started 21st and ended up 15th and ahead of Italy's 2018 Olympic gold medallist Sofia Goggia, who had a fall in final training on Friday.
Nursing a cold, Vonn had failed to finish Thursday's super-G after hitting a gate.
"I knew it wasn't a perfect run but I knew it was good," said Johnson, who missed the 2018-19 season and 2022 Beijing Olympics through injury and was in tears at the finish as she realised the gold was secure.
"Then when I came across the line and I saw it was a low 41, I was like 'amazing'."
Johnson has yet to win a World Cup race, with a best result of second but no podium since 2021.
"It's a privilege to be able to play the game, to be able to be here," she said of her return to competition and pre-event nerves.
"When you know that going in (to the race), you kind of have a little bit of freedom because you know that no matter what happens you've got a chance to try."
There was disappointment for Switzerland's Lara Gut-Behrami, the reigning Olympic super-G champion, who almost fell and failed to set a time.
Italian hopes were also dashed, with Goggia 16th and Federica Brignone, second in the super-G, only 10th. Austria's Stephanie Venier, the super-G gold medallist, was ninth.
The men's downhill is next up on Sunday.