Maze, who was fastest in the first run, beat Swede Frida Hansdotter by 0.34 after a second run in light snow as the Arctic sky darkened.
Austria's Kathrin Zettel had the day's fastest time of 56.70 to finish third, ahead of Sweden's Maria Pietilae-Holmner. Marie-Michele Gagnon of Lac-Etchemin, Que., was the top Canadian in sixth place.
Shiffrin, 14th after the first run, improved slightly in the second to finish 11th overall. The American had times of 59.83 and 57.39 for a 1:57.22 total, more than two seconds behind Maze.
Maze, double Sochi Olympic champion in downhill and the giant slalom, wasn't certain of winning on Saturday.
"I wasn't sure because I had made so many mistakes, not big mistakes but I didn't know where I would end up," Maze said. "But I'm like that sometimes. When I'm feeling good, I can ski well and get ahead."
Shiffrin leads the World Cup overall standings with 124 points, ahead of Zetel with 110. Maze is third with 109.
Gagnon is looking to make improvements so that she can win her third career World Cup medal.
"I'm starting to be a little fed up with finishing fourth, fifth and sixth," she said. "It's good to be there, but now I'm really looking forward to start being on the podium and being a little more in the game."
The 19-year-old Shiffrin was keen to analyze her performance.
"It's easy to win when you're winning. I still need to learn how to come back in the second run if I have a slower first run," Shiffrin said. "I still need to learn how to race like a champion. I wasn't able to do that today."
Maze was fastest in the first run with 58.12 seconds, 0.39 faster than Frida Hansdotter.
Known as one of the toughest slalom slopes on the circuit, Levi had a hard, gritty base after days of cold temperatures.
"The base is not icy but it's quite aggressive, making it hard to let your skis go," Hansdotter said.
Shiffrin, who won Olympic gold in the slalom at Sochi, was unbeatable at Levi last year. She skied a good first section in her first run but was slower on the steep part of the slope, trailing Maze by 1.71 before the second run.
Brittany Phelan of Mont-Tremblant, Que., did not qualify for the second run and Erin Mielzynski of Collingwood, Ont., did not finish the first run.
The men's slalom takes place Sunday at Levi, which is the world's northernmost World Cup venue, about 125 kilometres (80 miles) north of the Arctic Circle.
With files from The Canadian Press.Suggest a correction