Guay overcame steadily softening snow conditions on the rugged Kandahar course at Garmisch and finished with a time of 1 minute, 58.41 seconds, about one-third of a second ahead of Switzerland's Didier Cuche.
Christof Innerhofer of Italy took the bronze with Romed Baumann of Austria in fourth.
Steven Nyman was to top American in 13th place. Bode Miller clipped a gate early in his run and took 15th with a time of 2:00.38.
Nyman said Kandahar began falling apart early as the temperatures warmed up. "It's bumpy, it's icy, it's dark, that's the way Garmisch is," Nyman observed. "Guay won his first World Cup here and it was on this type of snow. He's the guy I look at for just clean, solid skiing and that's what won the race today."