Liut was the League's winningest goalie in the 1980s and a First-Team All-Star in 1980-81, when he helped the St. Louis Blues win the Smythe Division and finish second in the overall NHL standings.

The Blues selected Liut in the fourth round (No. 56) of the 1976 NHL Draft. He didn't arrive until 1979-80, when St. Louis reclaimed him from Cincinnati of the World Hockey Association prior to the 1979 NHL Expansion. He led the NHL with 32 wins in his first season, then went 33-14 with 13 ties in 1980-81, winning the Lester B. Pearson Award (now the Ted Lindsay Award), given to the most outstanding player as voted by members of the NHL Players' Association, and was second to Wayne Gretzky in voting for the Hart Trophy as the NHL's most valuable player.

However, the Blues were upset by the New York Rangers in the second round of the 1981 Stanley Cup Playoffs. Liut was also Canada's starting goalie at the 1981 Canada Cup, but was the losing goalie when the Soviet Union won the championship game 8-1.

Liut remained as the starter in St. Louis until Feb. 21, 1985, when he was traded to the Hartford Whalers. He was in goal when the Whalers won a Stanley Cup Playoff series for the only time in their history in 1986 and when they won their lone division title in 1986-87; he won 31 games that season and was named an NHL Second-Team All-Star.

The Whalers traded Liut to the Washington Capitals on March 6, 1990, and he helped the Capitals win three straight playoff games to advance to the conference final for the first time since entering the NHL in 1974. He was bothered by back problems during the next two seasons and retired in 1992.

Liut finished 293-271 with 74 ties, a 3.49 GAA, .883 save percentage and 25 shutouts in 663 games; his 251 wins were the most of any goalie in the 1980s. He was 29-32 with a 3.39 GAA, .889 save percentage and two shutouts in 67 playoff games.

Liut remained involved in hockey after retirement as a successful player agent.