Nicknamed "Tough Tony" and "Mighty Mouse", he was known also as a little pest, in part due to his small stature, at just 5'7" tall and 160 lbs.

Scoring 36 points in 19 games there, he followed up his great season by joining with HMCS Chippawa of the Royal Canadian Navy Reserve, where he helped to win the 1944–45 Basil Baker trophy for inter-service hockey.

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 enjoyed agitating opponents, including Maurice Richard of the Montreal Canadiens, and Gordie Howe of the Detroit Red Wings.

Detroit was impressed by Leswick's when playing against Gordie Howe, and acquired him after the 1950–51 season in a blockbuster trade on June 8, with Gaye Stewart going to New York.

Leswick was added to a line with Marty Pavelich and Glen Skov, and helped lead Detroit to Stanley Cup championships in 1952, 1954, and 1955.

Defenceman Doug Harvey went back to glove the puck, but instead deflected it past goaltender Gerry McNeil and into the net for the game-winning goal.

Following his third Stanley Cup victory in 1955, Leswick was traded to the Chicago Black Hawks along with Glen Skov, Johnny Wilson and Benny Woit for Jerry Toppazzini, John McCormack, Dave Creighton and Gord Hollingworth, on May 27.