Heinzer won at the world's most famous downhill venues: Kitzbühel (3x), Wengen, Val Gardena (2x), Garmisch, Val-d'Isère, Aspen, Lake Louise, and St. Anton. His victory in the downhill event at the 1991 World Championships came after three fourth places at previous championships (Schladming (1982), Bormio (1985) and Crans-Montana (1987). He didn't compete in the downhill at Vail in 1989. At the 1994 Winter Olympics in Norway, his right binding released at the starting gate, putting him out of the downhill race.