Running away with the title in the overall standings, Maze increased her lead to a massive 718 points ahead of Maria Hoefl-Riesch of Germany, who finished 19th.
"Today was a hard battle skiing down," Maze said. "It was snowing a lot and the snow stayed on the goggles. I didn't see a lot in the last part. I was just trying to stay on line, so I'm really proud of my performance today."
Vonn's American teammates, Julia Mancuso and Leanne Smith, finished fifth and sixth.
Vonn, a part-time Park City resident, had won the last four super-G races here and also won Saturday's downhill for her first victory since returning to the circuit from a three-week break to recover from an intestinal illness.
But the four-time overall champion was never in contention during her run, and when she reached the finish she just shook her head and shrugged her shoulders.
"It was difficult to punch in there today," Vonn said in a TV interview. "The snow was definitely soft and I got sucked a little bit low on the top section and I was able to make up time on the bottom, but it just wasn't enough."
In Wengen, Switzerland, Felix Neureuther of Germany won a World Cup slalom, defeating overall leader and training partner Marcel Hirscher of Austria. Neureuther made up a deficit of 0.05 seconds from the first run to beat Hirscher by 0.21 seconds and deny him a fourth straight slalom win.
Ivica Kostelic of Croatia was third, 0.25 behind Neureuther's two-run time of 1 minute, 50.53 seconds.
Ted Ligety of Park City, who is third overall, placed 13th, 1.33 behind Neureuther. Ligety earned 20 World Cup points and is 239 behind defending champion Hirscher.
In Calgary, Alberta, Sang-Hwa Lee of South Korea set a 500-meter world record in World Cup speedskating at the Olympic Oval.
Lee's time of 36.80 seconds lowered the mark of 36.94 set by China's Yu Jinh at the world sprint championships on the same oval last Jan. 29.
"I didn't expect the world record here," Lee said through an interpreter. "I was hoping to set it next week in Salt Lake City [at the world sprint championships]."
Other winners were Jens Smeekens of the Netherlands in the men's 500 and Heather Richardson of the United States and Hein Otterspeer of the Netherlands in the 1,000.
Germany's Maximilian Arndt led his four-man team to victory in a World Cup race in Igls, Austria, that also counted as the European bobsled championships.
Arndt and his team of Marko Huebenbecker, Alexander Roediger and Martin Putze were fastest in both heats at the 1976 Olympic track and finished in a combined time of 1 minute, 43.33 seconds.
They were 0.16 faster than second-place Switzerland, led by Beat Hefti, who won the European two-man bobsled title Saturday.
Another German team, led by Thomas Florschuetz, was 0.18 back in third.
Arndt now has 1,574 points in the World Cup standings and extended his lead over Zubkov to 47 points with one World Cup event in Sochi in February remaining.
The United States 1 team led by Park City's Steven Holcomb finished 17th, and the U.S. 2 team led by Nick Cunningham was 20th.