Hemsley became the starting catcher for the Browns in the 1934 season, and his best years were with the St. Louis Browns in 1934 and 1935, when he hit .309 and .290 respectively. He also hit 7 triples both years, a career high. His effort in 1935 also earned him his first spot on the All-Star team, as well as 9th place in MVP voting. He played well for two more seasons for the Browns, but a batting average of .222 in 1937, as well as a suspension for violation of team rules on July 2, 1937, led to a trade on February 10, 1938. Hemsley was traded to the Cleveland Indians for Ed Cole, Roy Hughes, and Billy Sullivan, Jr. on the recommendation of Bob Feller, who had been impressed with Hemsley's catching skills. He spent the 1938 season backing up Frankie Pytlak but, became known as Feller's personal catcher. Hemsley became the starter in 1939 after Pytlak went down with an injury, and played well enough to earn his third All-Star bid. On opening day of the 1940 season, Hemsley caught Feller's no-hitter, becoming the only catcher to catch an opening day no-hit game. He also drove in the only run of the game with a triple. His consistency in the 1940 season saw him lead the American League catchers with a .994 fielding percentage, and led to a couple MVP votes as well as his fourth All-Star appearance.