Hungate was admitted to the Missouri bar in 1948 and the Illinois Bar in 1949 and immediately entered private law practice in Troy, Missouri, from 1948 to 1968. He was then elected prosecuting attorney of Lincoln County, Missouri, serving from 1951 to 1956. From 1958 to 1964, he served as a Missouri Special Assistant Attorney General. On November 3, 1964, he was elected as a Democrat simultaneously to the 88th Congress to fill the vacancy caused by the death of Representative Clarence Cannon, and to the 89th Congress. He was reelected to the five succeeding Congresses, serving until January 3, 1977. Hungate voted in favor of the Voting Rights Act of 1965 but against Civil Rights Act of 1968.