Damphousse had a long NHL career as a consistent scorer, finishing with at least 20 goals in 12 of his 18 seasons, exceeding 90 points four times and helping his hometown Montreal Canadiens win the Stanley Cup in 1993.

The Toronto Maple Leafs selected Damphousse with the No. 6 pick in the 1986 NHL Draft after seasons of 103 and 155 points with Laval of the Quebec Major Junior Hockey League. He scored 21 goals as a 19-year-old NHL rookie in 1986-87 and topped that total three times in the next four seasons, including a 33-goal, 94-point season in 1989-90. The forward scored four goals in the 1991 NHL All-Star Game at Chicago Stadium and was voted the game's most valuable player.

The Maple Leafs traded Damphousse to the Edmonton Oilers on Sept. 19, 1991, as part of the deal that sent future Hockey Hall of Famers Grant Fuhr and Glenn Anderson to Toronto. But after finishing with 89 points (38 goals, 51 assists) with the Oilers in 1991-92, he was traded again, this time to the Canadiens on Aug. 27, 1992.

Damphousse continued to bump up his offensive numbers in 1992-93, leading the Canadiens with 97 points (39 goals, 58 assists), then scoring 11 goals (including three game-winners) and 23 points, both team highs, to help Montreal win the Stanley Cup. He followed that with an NHL career-high 40 goals and 91 points in 1993-94, and scored 38 goals during a 94-point season in 1995-96.

But Damphousse's scoring totals began to drop, and the Canadiens traded him to the San Jose Sharks on March 23, 1999.

Damphousse played his final six seasons with the Sharks, scoring at least 20 goals three times. He missed much of 2000-01 with injuries but finished with 46 points (nine goals, 37 assists) in 45 games.

Damphousse retired after 2003-04 with 1,205 points (432 goals, 773 assists) in 1,378 NHL games, and 104 points (41 goals, 63 assists) in 140 playoff games.