Glanzmann, who started for SC Marbach , was accepted into the national team in 1983 and made his debut in the Nordic Combined World Cup on December 29, 1983 in Oberwiesenthal . As the 45th he missed the top places and thus the World Cup points by a large margin. At the Nordic World Ski Championships in 1985 in Seefeld in Tirol , he finished fifth in the individual. In March he reached his first 22 World Cup points as 12th in Lahti and ninth in Oslo and thus reached 22nd place in the overall World Cup ranking. In the following 1985/86 season he also got clear points straight away in Tarvisio and Schonach in the Black Forest . He was third in Schonach for the first time on a World Cup podium. However, it was his last podium for a year. He finished the 1985/86 season in sixth place overall.
In the 1986/87 season he achieved his first and only World Cup victory in January 1987 in Reit im Winkl . Glanzmann was the first Swiss to win a Nordic Combined World Cup. He also finished second on the podium in the following World Cup in Autrans . Then he confidently traveled to the Nordic World Ski Championships in 1987 in Oberstdorf . There he reached fifth place in the team competition together with Hippolyt Kempf and Andreas Schaad . The 1986/87 season he finished a little later in 10th place overall.
At the 1988 Winter Olympics in Calgary , he won silver with the team. In the individual, he did not get above rank 35. With the Nordic World Ski Championships in Lahti in 1989 , Glanzmann finally contested his last major international competition and also won silver there with the team. From 1990 to 1992 he played a few more competitions in the B World Cup before ending his active career.