The win was Vonn's seventh of the season and pushed her over the 1,000-point mark in the World Cup standings, 302 points ahead of the second-place Maze.
Vonn turned in a combined-run time of 2 minutes, 28.35 seconds to top Maze, whose two-run time totaled 2:28.79.
Maze was 1 second faster than Vonn in the slalom portion of the race but the American had a big enough edge in the earlier downhill for the overall win.
"I felt like I had a really good downhill run but I was a little bit nervous," Vonn said. "I didn't think I had enough time ahead of the slalom girls but I put together a solid slalom run to hang onto the lead."
Austrians Nicole Hosp and Kathrin Zettel took third and fourth places.
Celebrity Families of 2014 [PHOTOS]