Fenninger was clocked in a two-run time of 2 minutes, 29.39 seconds at Ofterschwang, Germany.
She led Maze by 0.03 seconds after the first run and then turned up the heat with a 1:17.55 in the second run.
"I was quite surprised to see how fast I managed to ski in the second run, starting last", she said. "The conditions weren't as good as they were obviously in the first run."
Viktoria Rebensburg of Germany finished third.
Rain fell in Ofterschwang early in the morning but gave way to partial clearing by the time the racing started.
Maze, who leads the overall women's World Cup standings, finished in the top three for the eighth time in eight giant slaloms this season. Germany's Maria Hoefl-Riesch, who is second in the overall race ahead of Fenninger, finished 16th Saturday.
Julia Mancuso of the United States finished eighth.
"They did a good job of keeping the course OK," she said. "It was actually one of the better surfaces we've had this year. The second run was a lot 'turnier,' so it deteriorated and was difficult for racers starting in the back."