Maze finished the twisty course in 1 minute, 45.89 seconds to beat Anna Fenninger of Austria by 0.02 seconds. Lara Gut of Switzerland earned bronze.
This result was the reverse of the super-G race, when Fenninger won and Maze was runner-up. Maze has a chance to medal in every event at worlds.
"It's nice to be here and ski like that," Maze said. "This makes it fun. I'm happy I can be part of it."
Larisa Yurkiw of Owen Sound, Ont., was 14th.
Vonn got off to a fast start in the gliding portion, to the delight of the capacity crowd. But she faded in the curvy middle section and wound up fifth.
"Honestly, I did the best I could," said Vonn, who leads the World Cup downhill standings. "I fought the whole way down. I was so focused. I visualized the course a thousand times. It just wasn't a great run. It was a good run, but not a top-five worthy run. There's not a lot to be sad about."
Vonn's worlds aren't over, though. She said she will compete in the giant slalom and the Alpine combined, which meshes the times of a slalom run and a downhill run.
Racing No. 16, Fenninger had a clean run and jumped into the lead. Her teammate, Elisabeth Goergl, couldn't catch her. Neither could Gut.
Then along came Maze, who glided just a little better in the flatter sections and took over the lead by the slimmest of margins. Maze held her breath with Vonn going next, but the American scuffled in the technical sections.
Maze tied for the Olympic gold medal in Sochi with Switzerland's Dominique Gisin, who didn't compete in this event after cracking the tibia bone in her right knee during a crash on Jan. 19. Gisin made a quick recovery and may compete in the giant slalom next week.
Marion Rolland of France didn't get a chance to defend her downhill crown at worlds after tearing the ACL in her right knee in a mid-January crash during a super-G.