Maze held her morning lead to finish 0.08 seconds ahead of Viktoria Rebensburg, the Olympic champion from Germany, in a total time of two minutes 11.07 seconds. Tessa Worley of France was third, trailing Maze by 0.55.
Vonn hit trouble midway down her second run after her skis appeared to touch. The American racer came out of rough, course-side snow to complete the race nearly six seconds slower than Maze and score four valuable World Cup points.
"That's why I kept fighting to the end," said Vonn, who lost the overall title by just three points to Maria Hoefl-Riesch in 2011.
Marie-Michele Gagnon of Lac-Etchemin, Que., was 12th.
The win gave Maze 100 points and she now leads by 234 from Germany's Hoefl-Riesch, who placed ninth. Vonn is third, 263 behind Maze.
Maze's fourth victory this season — and second at St. Moritz this weekend — means she and Vonn have combined to win eight of the 10 events this season.
"For sure, it's challenging to be the first (place) skier and keep at this tempo," said Maze, who was a distant second in the overall standings last season as Vonn enjoyed a career-best year.
"We've been building for four years," the 29-year-old Slovenian said." I have power, stability, good material and good people around me."
Vonn said she was still struggling for full fitness after falling ill last month.
"I was just dead. Two-run races are really hard for me right now," she said. "I caught on the inside ski a little bit. Normally I should make this kind of recovery."
Vonn had enough energy to win Saturday's Super-G, raced on a shortened course because of high winds, when Maze was runner-up.
Their rivalry was stoked further Saturday when Maze's coaches wrongly alleged that the American directed an expletive at the Slovenian racer when she completed her victorious run.
Maze said the dispute was now settled with Vonn, who acknowledged she had sworn out of relief and tension.
"I felt bad because I was wrong," Maze said. "I said to Lindsey I am glad she didn't say the things I thought she said. I have respect for her and she has respect for me."
Maze got her 15th career World Cup win and 11th in giant slalom, one of two events in which she won silver medals at the 2010 Vancouver Olympics.
Vonn will hope to close the gap when her specialist speed events, downhill and super -G, are raced next at Val d'Isere, France.
"I have got to win every speed race," said Vonn, who was a perfect four wins so far this season. "I just have to rest up for next weekend. Right now, I'm definitely not feeling great."