Back to her best, the American beat the 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.
The Slovenian disappointed the crowd, who were hoping to see their favourite win after she comfortably dominated the first run.
Maze still has the chance of Sunday's slalom as a consolation prize 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.