He played for the Chicago Blackhawks, New York Rangers, Vancouver Canucks, St. Louis Blues and Phoenix Coyotes.
Originally selected in the 1983 NHL Entry Draft by the Chicago Blackhawks, Noonan played parts of seven seasons in Chicago, although during the middle part of his career with the Blackhawks he mainly saw playing time in the minors with the Indianapolis Ice.
Noonan would eventually regain a roster spot with the Blackhawks, especially after Mike Keenan became head coach.
Despite being credited to Mark Messier, the game-winning goal of game 7 of the 1994 Stanley Cup Finals was later shown to be scored by Noonan.
Noonan played for head coach Mike Keenan on four occasions; with the Blackhawks, Rangers, Blues, and Canucks.