The 29-year-old Swede led after the first run and did just enough to hold on for the win, clocking 1 minute, 49.55 seconds to beat Hirscher by just 0.06 seconds.
Myhrer, a 2010 Vancouver Olympics bronze medallist , earned the fifth World Cup slalom victory of his career, but said he was still nervous going out last after seeing Hirscher put down a good time.
"This level is so high so if you take it easy just a little bit you're behind," he said. "It's not easy to be alone up there ... knowing that everybody is down (already) and it's just you left. But I've proved that I can manage that."
Hirscher trailed by 0.27 seconds after the first run and had the second fastest time of all skiers in the afternoon as well.
"I'm happy, really happy at the moment," Hirscher said. "And six hundreds of a second is really nothing."
Jens Byggmark, also of Sweden, was 0.61 seconds behind in third for his first World Cup podium finish in four years. Byggmark burst onto the scene unexpectedly by winning back-to-back slaloms in Kitzbuehel in 2007 but has not won a major race since. He took silver at the world championships last year, and showed again on Sunday that he can still challenge for victories.
"I've been working really hard to be more stable and I think I've reached my goal," the 27-year-old Byggmark said, adding that he needs to "keep this level and to be on the podium for the whole season."
The Swedes have a new coach this season, former Alpine skier Johan Brolenius, whose training tactics have helped lift the team, Byggmark said. "We have a good pace (in) training and we're fighting, we're fighting hard, and we're helping each other."
American Ted Ligety, who won the opening giant slalom World Cup race in Soelden by the biggest winning margin since 1979, finished in a tie for 13th place, 1.65 seconds behind Myhrer.
Ligety is now third on the overall leaderboard. Hirscher is currently in the lead with 140 points and Italy's Manfred Moelgg is trailing a close second.
Levi — about 105 miles north of the Arctic Circle — is the world's northernmost World Cup venue.
Last year, the scheduled circuit races were cancelled here because of a lack of snow.
The next men's World Cup races are in downhill and super G in Lake Louise, Canada, on Nov. 24-25.