Swiss racer Gisin, wearing bib number eight, was first to clock one minute 41.57 seconds down the icy 2.7-kilometre-long course and in brilliant sunshine it looked to have been enough for outright victory.
But Gisin, 28, who has not won a World Cup downhill race since 2009 and whose best finish in the downhill this season is seventh, had not counted on Maze, the 2013 super-G world champion and proven big-stage performer.
Starting 13 runners after Gisin on a course that had not broken up, the Slovenian led all the splits but lost a little time after the final jump to come charging through the finish line in a dead heat.
Maze has had a relatively poor season, which was only partially rescued by a first downhill win in Cortina d'Ampezzo in January, but her third place finish in the downhill run of the super-combined was a reminder of her speed abilities.
"I'm extremely happy and completely overwhelmed," said a tearful Gisin, from Engelberg in the canton of Obwalden.
One onlooker left delighted was Maze's coach Mauro Pini, the former head coach of the women's Swiss ski team.
"Tina is a hard worker so this is nice for her," said Pini.
"I'm also happy for Dominique as she was my first athlete."
Gisin's gold was Switzerland's fifth women's downhill Olympic title and the first since Michaela Figini at the 1984 Sarajevo Games.
OMG! Gold!!was für ein tag…thank you all for the wonderful support, it's a dream, only better because it's the reality!
— Dominique Gisin (@dominiquegisin) February 12, 2014
— Marc Gisin (@marcgisin) February 12, 2014
There was more joy for the Swiss team when Lara Gut, who has so far this season won three super-G and one downhill World Cup race and finished second in the combined's downhill, claimed bronze, 0.10 seconds behind.
There was no silver awarded in the race marked by the absence through injury of defending champion and media darling Lindsey Vonn of the United States.
Germany's Maria Hoefl-Riesch, the winner of Monday's super-combined, could only finish 13th, and Austrian silver medallist Nicole Hosp ninth.
It meant Hoefl-Riesch, who stands atop the World Cup overall and downhill standings so far this season, missed out on drawing level with now-retired Croatian Janica Kostelic's record of four Olympic golds.
But the 29-year-old German will have other opportunities as she races in all five disciplines.
Other rivals for the downhill crown included a couple of racers who disappointed on Monday, including Austria's Anna Fenninger.
Fenninger finished eighth in the super-combined and suffered more woe on the Rosa Khutor course when she skied out after losing control in the middle section.
American Julia Mancuso, who had snatched bronze in the combined thanks to a fastest downhill run and won silver in the discipline in Vancouver four years ago, finished eighth.
"I am disappointed with my skiing, I made some big mistakes," said Mancuso.
"I would like to have another chance, but it's over. I have to move on to my next event.
"It's tough and really difficult to stay focused on the whole run, but that's what separates the champions from the rest of us on race day."