Leswick played his junior hockey in Saskatoon with the Dodgers and Quakers, and quickly started turning heads. In 1942, Leswick finally jumping into the AHL with the Cleveland Barons and scored 40 points in only 52 games. He moved onto the PCHL in the following season to play for the New Westminster Royals. Scoring 36 points in 19 games there, he followed up his great season by joining with HMCS CHIPPAWA of the Winnipeg Navy, where he helped to win the 1944–1945 Basil Baker trophy for inter-service hockey. The New York Rangers had seen enough and brought him into their lineup for the remainder of the 1945–46 season.
Professional career
Leswick scored 15 goals in his shortened rookie season for the Rangers and quickly established himself as one of the few bright spots in New York. He loved getting under peoples skin, including that of Montreal Canadiens' Rocket Richard, and Gordie Howe of the Detroit Red Wings. Leswick recorded consecutive 20-goal seasons in 1947 and 1948, but the Rangers continued to miss the playoffs or get knocked out in the early rounds. After scoring 44 points in 1949–50, he was named to the NHL second all-star team. During this time, he formed a successful combination with Edgar Laprade and Dunc Fisher. Detroit had seen the way that Leswick would go after Howe and knew that took guts. They decided to trade for Leswick after the 1950–51 season. On June 8, Tony Leswick became a Detroit Red Wing after a blockbuster trade that saw Gaye Stewart going to New York. Leswick would continue his pestering ways and was inserted on a line with Marty Pavelich and Glen Skov. He would help lead Detroit to Stanley Cups in 1952, 1954, and 1955. He is probably most remembered for his winning goal in game seven of the 1954 Stanley Cup finals against the Montreal Canadiens. Leswick had this to say in an interview with Chuck O'Donnell
"It was early in overtime, I don't know, maybe four or five minutes in. We were trying to change our forwards. I had the puck around centre ice or so and I just wanted to do the smart thing and throw it in. If I get caught with the puck and the Canadiens steal it, we may get caught and they may get an odd-man break. Just like that, the game could be over. So, I'm just thinking of lifting the puck down deep in their end, just making the safe play. So I flipped it in nice and high and turned to get off the ice. The next thing I know, everyone's celebrating. It had gone in. I said, "You've got to be kidding. It went in? Get out of here!""
Leswick tried his hand at coaching starting in 1958. He replaced the current coach of the Edmonton Flyers midseason in 1957–58 and would continue until midseason of 1958–59. He felt he was more of a help to the team on the ice. He would try his hand at coaching one more time with the Indianapolis Capitals/Cincinnati Wings of the Central Hockey League in the 1963–64 season. They would finish last in the league with a 12–53–7 record and Leswick would retire from the world of hockey.