In 1981, Hlinka and fellow Czech Jiří Bubla joined the NHL's Vancouver Canucks. This started the Czech migration to the NHL. They were the first Czechoslovak players to compete in the NHL with the permission of their country's authorities. (Jaroslav Jiřík played legally in the NHL in the 1969–70 season, but only in three games.) Playing in his first NHL season, Hlinka set a Canucks record for the most points by a rookie with 60 (later matched by Pavel Bure in 1991–92). During the subsequent 1982 Stanley Cup playoffs, the Canucks advanced to the Finals against the New York Islanders. In a losing effort (Vancouver lost the series in four straight games), Hlinka and Bubla became the first Czechs to ever play in the Stanley Cup Finals. The following season, Hlinka improved to 63 points over 65 games. In his two years in the NHL, Hlinka totalled 42 goals and assisted on 81 others in 137 games.