Maze turned in a winning combined-run time at Garmisch of 2 minutes, 20:54 seconds, 9/100ths of a second ahead of Italy's Federica Brignone.
Tessa Worley of France had the fastest time in the second run and finished third at 2:21.02.
Julia Mancuso was the top American finisher in 16th place. "In a GS, there are 50-60 gates and when you're on, you're on," said Mancuso. "If you're off, you add up those hundredths from all those gates and you've lost a second."
Maze was on from the beginning. She was first out of the starting gate in the first run and finished with a 1:07.05 and a comfortable lead over Brignone heading into the second race.