The overall World Cup leader from Slovenia sped down the Olympia course in the second run of a giant slalom to win in a combined time of 2 minutes, 23.84 seconds. It was her third win of the season and 26th of her career.
"Honestly I'd rather say 'Oh come on, just let me sleep.' But then I said (to myself) 'Come on, you took this program now you should get yourself together and do the races,'" said Maze, the Olympic champion in the giant slalom. "Sometimes you just have to push yourself over what your head is saying."
Maze was in seventh place after the first run, but she still finished .20 seconds ahead of Sara Hector of Sweden, who secured her first career podium. First-run leader Eva-Maria Brem of Austria was third, .28 behind.
Despite feeling sluggish, Maze was .70 faster than Hector and .86 faster than Brem on the second run.
"On the first run I didn't find the right pressure on the skis at the top," Maze said.
After fulfilling her media obligations, Maze laid down on the snow with her arms outstretched for several moments, already preparing to get some well-earned rest.
Feeling groggy actually seemed to help her to focus.
"I'm still jet-lagged. For sure you pay more attention on that ... if you're in that state of mind that you'd like to sleep," Maze said. "Sometimes things are coming to you really fast and sometimes when you're not focused the mistakes can happen."
Maze, who won the overall World Cup title in 2013, was 12th on the women's all-time list for World Cup wins.
She has shown her versatility this season, with a downhill win in Canada last month and victory in slalom in Finland.
"I'm probably the only one doing all events (this year)," Maze said. "It's amazing. I'm really happy about my skiing. I'm just relaxed."
Her form is picking up quickly after she made a difficult start to the season, finishing 22nd at the season-opening giant slalom in Soelden, Austria. She improved to fourth in giant slalom last month in Colorado.
"I didn't worry too much about Soelden, the others did more. I know I have something else," she said. "I expected a podium, I must say. I didn't expect a victory today."
Brem secured her third podium of the season — all in GS — after winning in Colorado and placing third in Soelden.
"I had my first podium here last year," Brem said. "For me, everything changed here."
Italian skiers Federica Brignone and Nadia Fanchini were fourth and fifth, respectively, while Anna Fenninger was sixth.
Marie-Pier Prefontaine of Ste-Agathe, Que., was 22nd.
Fenninger, the Olympic giant slalom silver medallist from Austria, was looking to become the first woman since Anja Paerson in 2004 to win five GS races in a calendar year.
A men's giant slalom under floodlights was to follow later Friday.
The women's race was moved from Courchevel and the men's from Val d'Isere because of a lack of snow in the French Alps.