After some successes in the youth field at national level, Resch started in the European Cup in 1978 and soon achieved his first top 10 results. In 1979 he won the downhill at the European Junior Championships in Achenkirch . On February 1st of the same year he made his debut in the World Cup and immediately won his first World Cup points with 15th place in the downhill from Villars-sur-Ollon . In the next winter he started mainly in the European Cup, where he achieved fourth place overall in the downhill classification with a win and a third place in the two downhill runs from Méribel .
From the 1980/81 season , Resch competed regularly in the World Cup and already achieved fourth place in the second downhill run on the Saslong in Val Gardena . After three more top 10 results, he celebrated his first World Cup victory again on December 13, 1981 in Val Gardena. Six weeks later he finished second on the Lauberhorn in Wengen , which also made him one of the medal contenders at the 1982 World Cup in Schladming . At the World Cup descent on the Planai , Resch won the bronze medal behind the winner Harti Weirather and the second-placed Conradin Cathomen , although he lost a ski pole shortly after the second split. This mishap happened to him twice in the World Cup, which is why he was at times dubbed "The One-armed Bandit".
Resch also achieved a victory, this time in Val-d'Isère , and a second place in the 1982/83 World Cup season , and as in the previous year he was fourth in the Downhill World Cup this winter. The 1983/84 season , which Resch began in Schladming with his third World Cup victory , was even more successful . In January, three podium places followed in Wengen, Kitzbühel and Garmisch-Partenkirchen . Overall, he was among the top six in seven downhill runs and thus achieved second place in the Downhill World Cup behind the Swiss Urs Räber . He missed a possible victory in the Downhill World Cup due to a fall in the last race in Whistler . Ironically, at the highlight of the season, the 1984 Winter Olympics in Sarajevo , he was unable to confirm his good World Cup results. With eleventh place and almost 1.5 seconds behind the winner Bill Johnson , he had to accept a serious disappointment.
On December 13, 1984, Resch suffered a cruciate ligament rupture while training in Val Gardena , which is why he was unable to take part in any competitions during the entire 1984/85 season. In the next winter he again achieved three podium places (third place in Schladming and second place in each of the two downhill runs on the Streif in Kitzbühel), which made him seventh in the Downhill World Cup. In the 1986/87 season he finished on the podium twice in January (third place in Laax and second place in Kitzbühel), but at the highlight of the season, the 1987 World Cup in Crans-Montana , he fell far short of expectations with 16th place. Months later he had to interrupt his career for a year after a new injury when he suffered a broken fibula and a torn ligament in his right ankle while training in Obertauern on November 23, 1987 . After this second serious injury, Resch did not find his way back to his old form. In the next three years he was in the top ten in the World Cup several times, but top results did not materialize, which is why he was not used in the downhill at the 1989 and 1991 World Championships. At the 1991 World Championships , however, he was able to start in the combination in which he no longer competed in slalom after eighth place in the downhill. After the 1990/91 season, he ended his career at the age of 30.
In December 2004 Erwin Resch opened a ski and sports center under the name FRESCH: UP with his company: Bergsport Resch GmbH, on Katschberg .