Stubblefield was elected to the Kentucky Railroad Commission in 1951 and re-elected in 1955. In 1958 he sought election to the United States House of Representatives from Kentucky's 1st district in the far western part of the state. Stubblefield defeated the incumbent Congressman Noble Jones Gregory in the Democratic primary and won the seat in the general election. After winning the election Stubblefield resigned from the Railroad Commission on December 31, 1958, in preparation for his service in Congress. Stubblefield won election to the House in 1958 and began his service on January 3, 1959. Stubblefield won re-election seven times, serving eight terms. Stubblefield unsuccessfully sought re-election to his House seat in 1974 but lost in the Democratic primary to state senator Carroll Hubbard who went on to win the general election.
After leaving the House Stubblefield returned to Murray, where he is buried in the Murray City Cemetery. He was a distant cousin of inventor Nathan Stubblefield.