In his rookie season in the Majors, with the reigning world champion 1943 Cardinals, Klein was a strong contributor to the Redbirds' successful defence of the National League pennant.

Throughout the spring of 1946, the Pasquel brothers of the Mexican League had been making enticing offers to many low-paid Major Leaguers perpetually bound to their teams by the reserve clause.

In an attempt to slow this exodus, Chandler banned all players who broke their existing contracts to join the Mexican League, including Klein, from Organized Baseball for a span of five years.

The Sporting News reported that he paid $1,500 out of his own pocket to buy his release from his independent club in the Quebec Provincial League to rejoin Organized Baseball.

Then, in 1961, he was named to the infamous College of Coaches—a brainchild of owner Philip K. Wrigley, who decided to abolish the position of field manager and instead rotate "head coaches" to run the Cubs and their minor league affiliates.

In 1962, Klein was named head coach again, replacing El Tappe and managing 30 games between May 1 and June 3 (posting a 12–18 record).

In 1965, Klein was named to a third stint as head coach, replacing Bob Kennedy on June 14 and staying on through the rest of the season.