Maze was part of the first gold medal dead heat in Olympic alpine skiing history last week, finishing with the same time as that of Dominique Gisin of Switzerland.
In this competition she won by just .07 of a second over Anna Finninger of Germany, the first-place finisher in the super-giant slalom three days ago.
Maze, fifth in the overall standings on the World Cup circuit this season, had the best time in the first of two runs that make up the giant slalom. She led Sweden's Jessica Lindell-Vikarby by .52 of a second and Italy's Nadia Fanchini by .65.
Fenninger was fourth after the opening run and as skiers began to struggle in the rainy conditions, it appeared Fenninger might be able to rally to a victory.
Lindell-Vikarby turned in only the 20th quickest second run and dropped back to a final seventh-place finish. Fanchini had the seventh-fastest run in the second trip down the course and she dropped out of medal contention.
When Fenninger's time of 1:18.21 was shown on the scoreboard, Maze knew she would have to travel the course in at least 1:19:06 to win the gold. She was timed in 1:18.99, the 11th best effort in the second run.
The bronze went to Viktoria Rebensburg of Germany, who was seventh after the first run and then had the best time in the field for the second.
Fanchini was fourth and American phenom Mikaela Shiffrin was fifth. It was the first Olympic race for Shiffrin, who will turn 19 next month and who leads the World Cup slalom standings. She will go for a slalom medal on Friday.