Maze was already runner-up to Vonn in the overall standings last year, but she failed to win a race and trailed the American by a massive 578 points.
The Slovenian skied a perfect first run and held on to her lead in the second to finish in an overall time of 2 minutes, 31.41 seconds for her 12th career victory and first since winning a slalom in Lenzerheide, Switzerland, in March 2011.
"It's a very special day," Maze said. "This really makes me so happy."
Marie-Michele Gagnon of Lac-Etchemin, Que., was sixth and Marie-Pier Prefontaine of Saint-Saveur, Que., was 19th.
“It’s definitely a really good start to the season,” said Gagnon. “I didn’t come in with many expectations. I’ve been skiing well but I was just hoping for (a) top-30 (finish) really."
Erin Mielzynski of Guelph, Ont., didn't qualify for the second run.
Vonn was 2.37 seconds off Maze's time before she went out in the second run after hooking a gate with her left arm and sliding off-course.
"It was weird. I hit my hand at the base of the gate," Vonn said. "It hurts a little bit so I am going to have it checked out but I think it's OK. It happens sometimes in GS. Unfortunately I had no chance of continuing."
Maze put herself in contention for the victory with what she called "an incredible" first run.
"In the second run, I was fighting like everybody else as the conditions were not easy," Maze added, referring to thick fog over the course that forced organizers to delay the start by an hour. When the final leg did start, wet snow began to fall and made visibility even worse.
Many racers struggled and Olympic GS champion Viktoria Rebensburg of Germany and France's Tessa Worley were among the favourites who failed to finish their run.
However, conditions did not hamper Maze, who won here in 2002 and 2005. She beat second-place Kathrin Zettel by 0.42, and her Austrian teammate Stefanie Koehle trailed Maze by 1.71 in third.
"We have trained a lot over the summer but in the end, you just need to have fun," said Maze, who in the off-season changed the serviceman that prepares her skis. "Last year I had a poor start to the season and was fighting all the time to get going. It was no fun."
Vonn, who won her first GS race here last year, struggled in the middle part of her run. The four-time overall champion lost pace as she had to adjust her line in the steep section before bouncing back with a strong finish.
"I was really trying to push the limit in the second run," Vonn said. "I was pretty fired up over the first run. I didn't ski as aggressively as I needed to. I felt like I skied solid. The position on the skis was really good. I just didn't push the line enough."
Vonn said her surprise win from 2011 was still on her mind and she put pressure on herself to repeat the feat.
"I was honestly really nervous going into this race," she said. "I just didn't push it enough and you really have to do that on this pitch. In general, I am positive, I am skiing well, I know that, I just have to fix some tactical errors."
It was the first race under new equipment rules, forcing racers to use longer but smaller skis with a larger radius. The rule change, however, seems to affect the men more than the women.
"The new material is great and I feel really well," Maze said.
Vonn's American teammate Julia Mancuso lost her right ski after a solid start and failed to finish.
"It's one of those situations where nine out of 10 times your ski might stay on," Mancuso said. "I was going to make a transition, (it's a) bumpy slope, ski caught the other ski and just clipped off."
Mancuso was 0.18 behind Maze's first intermediate time when her run ended going into a left turn.
Mancuso switched her equipment supplier to join Vonn at Head in the off-season. She said the skis under the new rules were suiting her.
"I felt comfortable," Mancuso said. "We had a pretty reasonable course set this run ... just a really easy rhythm. I think you will get into bigger problems with these skis if it's really tight or just one difficult turn."
A men's GS on the Rettenbach course is scheduled for Sunday. The women's World Cup continues with a slalom in Levi, Finland, on Nov. 10.
With files from The Canadian Press.