Maze's combined winning time of 2 minutes, 13.54 seconds was a mere 0.018 second better than Vonn. Riesch took third Friday with a 2:14.09.
"Super combined titles are not easy to win because there are only three races so you can't make any mistakes," said Vonn.
Vonn led after the downhill leg of the event but Maze captured the slalom.
"I knew that it was really close with the points and I knew I had to ski a great slalom run to get the title," Vonn said. "I don't think it was my best slalom run, but I was aggressive the whole way and that was my goal."
Notable deaths of 2014 [PHOTOS]