The race was won by Tina Weirather of Liechtenstein in one minute 40.94 seconds, 0.51 ahead of Fenninger with Maze in third, a further 0.40 adrift.
It was the first time in five races that the Austrian World Cup holder had lost but the main thing was to finish ahead of the 2013 big globe winner as has repeatedly been the case in recent weeks.
"There is nothing like a fight like this to give you motivation. You must never say never but it's still going to be a close decision," Fenninger told reporters.
"Anna skis much too well right now. But I'll keep fighting until the end. This is a great chase," Maze said.
Crowned giant slalom and Super-G world champion in Beaver Creek last month, Fenninger is also a threat to Lindsey Vonn in the downhill standings.
The American, bidding for a seventh crystal globe in the discipline, finished sixth and now leads the Austrian by 39 points with one last downhill to be held at the World Cup finals in Meribel at the end of the month.
"It is quite a battle with Lindsey as well but she's very strong and I really can't say how it will turn out. I must also beware not to spend too much energy," Fenninger said.
"I really want to win the downhill World Cup. It would mean so much to me after my two operations," Vonn added.
Sunday's Super-G on the same Kandahar piste will be another decisive race for the three leading protagonists of the women's World Cup, Vonn still hoping to lift the specialty's title while Maze cannot afford to lose more ground on Fenninger.
"I'm OK. I've trained all summer to be able to make a great show until the Meribel finals," Maze said.
In the men's World Cup, Norway's Kjetil Jansrud lost vital points as he could only manage seventh place in a downhill on home snow in Kvitfjell.
Jansrud is now 152 points behind Austria's Marcel Hirscher in the overall standings and he retains a slim 20-point edge over the day's winner, Hannes Reichelt of Austria, in the downhill World Cup classification.
"Hannes is on a cloud right now," Jansrud told reporters.
"I still want to win both the Super-G and downhill globes and it would be a great disappointment if I failed after leading for most of the season."
Super-G world champion Reichelt had won two previous downhills this season in Wengen in January and Garmisch-Partenkirchen last week.
(Writing by Francois Thomazeau; editing by Ed Osmond and Michael Hann)
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