American Vonn, back to her best, beat the overall World Cup runaway leader by 0.08 seconds with a combined time of two minutes 22.20 seconds to snatch only the third giant slalom win of her career.
It was Vonn's 59th World Cup victory and a boost to her confidence ahead of the world championships in Schladming next month, when Maze will defend her crown in the discipline.
Maze's second place was enough for her to secure the giant slalom World Cup.
"It's my first crystal cup so I'm really happy,", said Maze, who had looked miserable when she crossed the finish line.
"I really wanted to thank the spectators with a big victory," added Maze who had set the fastest first-leg time. "I'm sure they must be happy with my second place. I fought as hard as I could."
Maze still has hopes of winning Sunday's slalom here and has increased her overall World Cup lead, leaving Germany's Maria Hoefl-Riesch 748 points adrift.
Austria's Anna Feninger continued her fine recent form to finish third, 0.57 off the pace.
Vonn, who took three weeks off over New Year to deal with health and personal problems, was delighted with her day's work.
"I had not skied a giant slalom for a month," the four-times World Cup winner said. "I was hoping for a good result but not to win but this course perfectly suits my style.
"The timing for the world championships could not be more perfect. This is a highlight after a tough moment. It also convinced me I could do well in giant slalom and I will race in four events at the worlds," she added.
With one title sewn up, Maze said she had plenty of other objectives.
"I was going for two wins here and I really hope I can do well in the slalom tomorrow. Then this was my 16th podium of the season and I heard that the record was 18," she told reporters.
"There's also the 2,000 points mark (in the overall World Cup standings) that Lindsey wanted so bad last season. There's a good chance to break it."
Maze is on 1,554 points with 13 races left until the end of the season, with each win being worth 100 points.
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