Maze parlayed a sizzling first run into a combined time of 2 minutes, 16.84 seconds, which was good enough to hold off Kathrin Zettel of Austria.
Zettel turned in a solid second run but finished 0.22 seconds behind Maze, who maintained a comfortable lead in the women's overall World Cup standings.
Maze said her success was a bit of a surprise even to her. "I'm just trying to be simple and enjoy my time on skis and not think of making history," she said after the race. "I'm even amazing myself."
Tessa Worley of France placed third Sunday and Julie Mancuso of the United States grabbed sixth place with a time of 2:19.17.
American Lindsey Vonn, who is second in the overall standings, fell on the first run Sunday and did not finish the event. She had crashed Friday during the downhill.
Swim Week Miami Beach 2014 [PHOTOS]