Maze, the overall World Cup points leader, finished in 1 minute, 35.39 seconds, topping Lara Gut of Switzerland by 0.38 seconds and Julia Mancuso of the United States by 0.52 seconds.
The race was marred by a spectacular crash caused by a lost ski that sent American Lindsey Vonn, who had been among the favorites in the event, to a hospital.
While Vonn's prospects for the remainder of this week's competition at Schladming remained in doubt, the win in the first event got Maze off on the right foot.
"This is very important for me," said Maze, "It is my first speed medal. I came here as one of the top favorites and this proved I am in good shape."
The race got off to a late start due to fog, but snow conditions on the lengthy 2,218-meter (1.4 mile) course were described as smooth and accommodating to aggressive tactics. "It wasn't a perfect run for me," said Gut, who last medaled at a World Championship in 2009. "I wasn't doing all that great throughout the slope and am not a super skier on such smooth snow, however, I felt like letting it go and giving it my best."