Quint was drafted 30th overall by Winnipeg in the 1994 NHL Entry Draft As a rookie in the 1995–96 season, by scoring two goals in a four-second span, he tied an NHL record originally set by Nels Stewart of the Montreal Maroons in 1931. The next season the Jets became the Phoenix Coyotes and Quint remained with Phoenix until he was traded to the New Jersey Devils on March 7, 2000 for Lyle Odelein. Quint would only play four regular-season games for the Devils before being traded to the expansion Columbus Blue Jackets on June 23 the same year where he stayed for two seasons leading the Blue Jackets in minutes played per game. For the 2002–03 season, Quint rejoined the Coyotes for a second campaign, and he later joined the Chicago Blackhawks the next season.