Primarily a power racer, Wiltrud Drexel made her World Cup début in 1968, and in January 1969 won her first two World Cup races, both downhills, one in Grindelwald (SUI) and one in Schruns (AUT). During her career she would make 27 podiums in World Cup, 20 of those in the downhill, winning five downhill races. In 1968-69 she won the downhill World Cup, her only seasonal title. She had five seasonal podiums in World Cup – 1968-69 and from 1970-74. She added an overall bronze medal for the 1968-69 season.
At the 1972 Winter Olympics Drexel took a silver in the giant slalom, but was not chosen for the Austrian team for her best event, the downhill, although in 1974 she won bronze at the World Championships in the downhill. Drexel won four Austrian national titles – the downhill in 1970, 1974, and 1976 and a slalom title in 1974. She failed to make the Austrian team for the 1976 Winter Olympics and retired after that season. She later settled in Warth in Vorarlberg, where she ran a boarding house. In 1996 Drexel was given a gold medal for her services to the Republic of Austria.