He spent one season playing at Boston College, starring on a team which won the National Championship and was loaded with players headed to the NHL.

During the 2004–05 NHL lockout, Kobasew played with the American Hockey League (AHL)'s Lowell Lock Monsters, and helped the team reach a number of franchise records.

On February 10, 2007, Kobasew and Andrew Ference were traded by the Flames to the Boston Bruins in exchange for Brad Stuart and Wayne Primeau.

Kobasew was traded by the Bruins to the Minnesota Wild in exchange for Craig Weller, a second round pick in 2011, and the rights to prospect Alexander Fallstrom on October 18, 2009.

[6] Whilst entrenched on the Avalanche in a checking line role, Kobasew appeared in his 500th game, along with linemate Jay McClement, on December 8, 2011, against his original club, the Calgary Flames.

Kobasew signalled the end of his NHL career, in signing his first European contract on a two-year deal with Swiss club, SC Bern of the National League A (NLA) on July 1, 2014.