The Slovenian, who has also won a super-combined, clocked a two-leg time of two minutes 16.84 seconds to pull ahead in the overall World Cup standings.
Austria's Kathrin Zettel had to be content with the runner-up spot for the third time this season, 0.22 seconds behind Maze, while local favourite Tessa Worley was third, 0.40 behind.
Maze's streak of four wins was the first such run in giant slalom since 2008 when Italy's Denise Karbon pulled off the feat.
"I remember clearly that year when Karbon won everything," Maze said. "It's great but I would love to win six."
Maze's 16th World Cup victory enabled her to take a lead of 331 points over Maria Hoefl-Riesch in the race for the overall trophy, while Zettel lies third, 28 points behind the German.
The Slovenian's 799 points represent the highest tally at this stage of the season.
"Who could have said at the start of the season that I would hold that many points? It looks natural because I ski so well, but there's a lot of hard work behind each and every point," she said.
The Slovenia's ambitions were boosted by a new disappointment for World Cup holder Lindsey Vonn, who failed to complete the first leg and headed straight back home to the United States for a rest over Christmas.
"Hit a rock on my left ski in the GS and skied off course," Vonn wrote on her Facebook page.
"Struggling to find the energy I usually have... going to think hard over the next few days about my plan for the coming weeks and how to get strong again. Trying to stay positive."
The American four-times World Cup winner would not return before the St Anton downhill on January 12, a U.S. Ski Team spokesman said.
Maze said it was a pity not to be able to compete against an in-form Vonn.
"It's true that it's not the same when the leading skiers are not all there, but I'm really tired as well. I will again have to grit my teeth until Are," she said.
The women's circuit moves to the Swedish resort for two technical races on Wednesday and Thursday.
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- Kathrin Zettel
- Denise Karbon