Born in Nitro, West Virginia, Burdette was signed by the New York Yankees in 1947, and after making two relief appearances for the team in September 1950, he was traded to the Braves in August 1951 for four-time 20-game winner Johnny Sain. Along with left-hander Warren Spahn and right-hander Bob Buhl, he gave the Braves one of the best starting rotations in the majors during the 1950s, winning 15 or more games eight times between 1953 and 1961. Burdette led National League pitchers in earned run average in . When Milwaukee won the 1957 World Series against the Yankees, Burdette became the first pitcher in 37 years to win three complete games in a series, and the first since Christy Mathewson in 1905 to pitch two shutouts (Games 5 and 7). In the 1958 Series, however, the Yankees defeated Burdette twice in three starts. The final setback came in Game 7, which he started on only two days' rest, a decision for which manager Fred Haney was widely criticized. In addition to winning 20 games in and tying Spahn for the National League lead with 21 victories in , Burdette won 19 in 1956 and 1960, 18 in 1961, and 17 in 1957.