The Slovenian finished 0.42 seconds ahead of Kathrin Zettel at the Tyrolean resort with fellow Austrian Stefanie Koehle in third.
It was a 12th World Cup win for the 29-year-old who held a .74 second lead over France's Tessa Worley following the first run before holding on to an advantage in the second run which was delayed due to fog.
Both Worley and defending World Cup discipline champion Viktoria Rebensburg, third after the opening stanza, skied out in poor visibility but the world GS gold medallist produced a composed run to hold off Zettel.
"I set myself high goals this winter and aim to fight for the overall title," Maze, who won in a combined time of two minutes 31.41 seconds to become the first woman skier to achieve three wins on the Soelden glacier after victories there in 2002 and 2005, said.
It was a relief for the 29-year-old Slovenian, who did not win a World Cup race last season despite several podium placings.
"This is a super day and a super win for me. It's exciting to start the season with that great win as I trained very hard in the summer with my group," she said.
"This takes much weight away from my shoulders," she added.
Maze, who progressed steadily in the overall World Cup standings from fourth in 2009, third in 2010 and runner-up last year, last won a race in Lenzerheide in March 2011.
Zettel produced the fastest run of the second leg while team-mate Koehle enjoyed a personal best as she climbed from 11th place after run one. They were both sporting black armbands to mourn the loss of young Austrian team mate Bjorn Sieber in a car crash earlier this week.
Lindsey Vonn, who won the race last year and beat Maze into second place in the overall World Cup standings in 2011/12, was down in 12th after the first run and then crashed out on the second after clipping a gate with her arm.
Vonn, the second most successful woman skier in the history of the sport, made headlines before the start of the season when she wrote to the International Ski Federation asking to be allowed into the men's downhill in the Canadian resort of Lake Louise on November 24.
"It was definitely not in the game plan what happened today," the American said. "I was trying hard but my arm got caught in the gate and the visibility was very bad."
The men's giant slalom takes place on Sunday.
- Sports & Recreation
- Kathrin Zettel
- Tessa Worley