In Klassen's ten-year career, he played for the California Golden Seals, Cleveland Barons, Colorado Rockies, and St. Louis Blues.
Klassen played his entire major junior career with the Saskatoon Blades of the WCHL, where he skated for five seasons, as a center and left wing.
Klassen made his NHL debut as one of two youngest players on the squad at the age of 19, along with Dennis Maruk, on October 8, 1975, at the Atlanta Flames.
A solid two-way player, he was a consistent contributor to the team; however, it did not help the dismal play of the hapless Barons who won only 47 games in their two NHL seasons.
In the 1977–78 season, after playing 13 games for the Barons, he was traded to the Colorado Rockies on January 9, 1978, as part of a deal with Fred Ahern for Chuck Arnason and Rick Jodzio.
Klassen was sent down to the minors, where he split the year playing 18 games for the Philadelphia Firebirds, Colorado's affiliate in the American Hockey League.
After his NHL career, Klassen resided in Saskatoon, Saskatchewan, working as a mail carrier for Canada Post.