He was drafted by the Quebec Nordiques in the fourth round (87th overall) of the 1986 NHL Entry Draft. He was primarily used as a backup during his first three pro seasons, bouncing up and down between the Halifax Citadels of the American Hockey League (AHL) and the parent club in Quebec City. During 1990–91 NHL season, Tugnutt played what would be a career-high 56 games for Quebec and established himself as a quality NHL starter despite playing for what was then the worst team in the league.