Overstreet's musical career started when he was 17, singing on country and western star Slim Willet's television show in Abilene. In the late 1950s, Overstreet started a group called "The Shadows."

He first recorded at Norman Petty's studio in Clovis, New Mexico, along with Jimmy Gilmer and the Fireballs. In 1960, Overstreet recorded in New York City at Roulette Records, with Doc Severinsen on trumpet, Sam "The Man" Taylor on saxophone and the Ray Charles Singers singing backup.

In 1967, Overstreet was hired to manage Dot Records in Nashville, Tennessee. In 1970, he decided to pursue a recording career, quickly establishing himself as a country hit maker that very year with a top five hit, "Gwen (Congratulations)," which peaked at No. 5 on the Billboard country music chart.

Overstreet made frequent guest appearances on the TV variety show Hee Haw. His highest charting Billboard hit was 1972's "Ann (Don't Go Runnin')," which went to No. 2.

His other top-20 hits were "I Don't Know You Anymore" (#5 in 1971), "Heaven is My Woman's Love" (#3 in 1972), "Send Me No Roses" (#7 in 1973); "I'll Never Break These Chains" (#7 in 1973), "(Jeannie Marie) You Were a Lady" (#7 in 1974), "If I Miss You Again Tonight" (#8 in 1974), "I'm a Believer" (#9 in 1975), "That's When My Woman Begins" (#6 in 1976), "If Love was a Bottle of Wine" (#11 in 1976), "Don't Go City Girl on Me" (#5 in 1977), "Yes, Ma'am" (#12 in 1978, and "Fadin' In, Fadin' Out" (#11 in 1978).