Evans was born in Denton, Texas, but spent some of his childhood in Kansas City, Kansas, where his cousin Eddie Durham was a trombonist and guitarist. Durham persuaded him to switch from alto to tenor saxophone, the instrument that ultimately established Evans’s reputation. After perfecting his craft in the jam sessions held in the jazz district between Twelfth and Eighteenth streets in Kansas City, Evans returned to Texas in the 1920s and joined the Troy Floyd orchestra in San Antonio in 1929. He stayed with this territory band until it dispersed in 1932. Evans performed for a time with Lionel Hampton and Buck Clayton in Los Angeles, and in the mid-1930s returned to Kansas City to become a featured soloist in Count Basie’s big band.

Evans also made records with jazz musicians such as Harry James, Teddy Wilson, and Lionel Hampton. Evans has been credited with influencing fellow tenorist Buddy Tate — who, in 1939, came from the Nat Towles band in Omaha to replace Evans in the Basie band when he died He is also credited for influencing Illinois Jacquet and Arnett Cobb. Although not a prolific composer, Evans wrote a number of well known pieces, including “Texas Shuffle” and “Doggin’ Around.”

Basie’s recording session in New York with Decca on January 5, 1939, was Evans’ final recording.

Edgar Battle sued Lewis Publishing Company in 1952 for failing to adequately promote songs that he published with them.