Steve Dubinsky was selected 226th overall in the 1990 Entry Draft by the Chicago Blackhawks.
In 1989-90, he enrolled at Clarkson University and scored 17 points as an ECAC freshman. The following season, he improved to 36 points. In 1991-92, Steve scored 20 goals and 51 points. In 1992-93, he scored 18 goals and 44 points.
In 1993-94, Dubinsky got into the Hawks' lineup for 27 games and appeared in six playoff games. In the shortened 1994-95 season, he played in 16 games.
By the 1995-96 season, Dubinsky was inserted into 43 games but his breakthrough season came in 1997-98 when he dressed for all 82 games and scored 18 points. He won the Norelco Face-Off Award for the month of October.
Dubinsky was traded on October 27, 1998 with Jeff Shantz to the Calgary Flames for Marty McInnis, Jamie Allison, and Eric Andersson. In 62 games between the two teams, he scored 14 points. He saw limited action in the 1999-2000 season because of a knee injury.
On August 25, 2000, Dubinsky signed as a free agent with the Chicago Blackhawks. In his first season back with the Blackhawks, he produced ten points