After a stellar junior career with the Ottawa 67's, Potvin was drafted to the NHL first overall of the 1973 NHL Amateur Draft by the New York Islanders, who had just established league a league record for the worst season record ever. Potvin became an instant hit in the league, earning the Calder Memorial Trophy. His brother Jean Potvin also played in the National Hockey League; they played together in New York for roughly 5 seasons. Their cousin Marc Potvin also played in the NHL.