Maze won the event by a 0.42 second margin over Kathrin Zettel of Austria and well ahead of third-place Austrian Stefanie Koehel.
Maze turned in a nearly flawless first run at Soelden and battled through the second to finish with a combined time of 2 minutes, 31.41 seconds.
"I had a good lead from the first run, and that is why I was trying to be more relaxed even if I was making some mistakes," Maze said afterward. "Normally, I would panic."
The win was Maze's third career victory at Soelden and her first since 2005.
The U.S. team had a rough time Saturday. Julie Mancuso lost a ski on the first run and Lindsay Vonn hooked a gate on the second and stumbled to 12th place.