Duguay played junior hockey for his hometown Sudbury Wolves of the Ontario Major Junior Hockey League, his 134 points (42 goals, 92 assists) in 1975-76 helping them win the Hamilton Spectator Trophy as the team with the best record in the regular season (47-11 with eight ties) and the OMJHL finals, a six-game loss to Hamilton. He was selected by the Winnipeg Jets with the No. 3 pick in the 1976 World Hockey Association Draft, played for second-place Canada at the 1977 IIHF World Junior Championship and joined the Rangers directly from juniors after they chose him in the first round (No. 13) of the 1977 NHL Draft.
The 1978-79 Rangers, guided by coach/general manager Fred Shero with future Hockey Hall of Famer Phil Esposito and a young core that included Duguay, Ron Greschner, Steve Vickers, Dave Maloney, Don Maloney and Don Murdoch, went 40-29 with 11 ties to clinch a playoff berth for the first time in two seasons. Led by goalie John Davidson, New York eliminated the Kings and Philadelphia Flyers and upset the top-seeded New York Islanders in six games of the NHL Semifinals to advance to the Final. Duguay became famous for his long, curly hair flowing while he skated without a helmet, and joined Esposito, Dave Maloney and Anders Hedberg in a 1979 Sasson jeans television commercial known for the jingle, “Oo La La! Sasson.”
Duguay scored nine seconds into an 8-3 win against the Flyers at the Philadelphia Spectrum on April 6, 1980, to tie a Rangers record shared by Fred Cook (Jan. 23, 1927) and Jean Ratelle (Nov. 5, 1971). He was traded to the Red Wings on June 13, 1983, reunited with the Rangers via a trade with the Penguins on Jan. 21, 1987, and played the final two seasons of his NHL career after he was sent to the Kings on Feb. 23, 1988.