She was as solid in the second run, winning by 0.07 seconds in 2:36.87.
Super-G champion Anna Fenninger of Austria claimed her second medal with silver while German defending champion Viktoria Rebensburg won bronze.
Vanessa-Mae's Olympic skiing debut
competing for Thailand as Vanessa Vanakorn, was the 67th and last finisher on her Olympic debut with a time of 3:26.97 - 50 seconds behind Maze.
The Slovenian, who won silver in giant slalom and super-G in Vancouver four years ago, led Sweden's Jessica Lindell-Vikarby after run one and held on despite only posting the 11th fastest time in the second descent.
She celebrated by belly-flopping onto the wet snow and pretending to swim the breaststroke.
"I have dreamed about a day like this, even though it is raining," she said. "I feel proud, I think I will realise what I have done many years later."
Maze is the oldest Olympic women's giant slalom champion and the second female to do the downhill-giant slalom double at a Games after Switzerland's Marie-Therese Nadig in Sapporo in 1972.
American Julia Mancuso, who won bronze in the combined event, crashed out on the first run, while Germany's double Sochi medallist Maria Hoefl-Riesch pulled out ahead of racing with a sore throat.
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