Burton was born in Indianapolis, the son of Bonnie L. (née Hardesty) and Charles W. Burton. His father, a former policeman, was abusive to his mother, and never held a job for very long. The family moved constantly, living in trailer parks, cabins, and motels. In June 1950, some years after the couple divorced, his mother went to the police and got a restraining order against his father. He responded by kidnapping Burton's mother. Burton and his younger brother and sister were briefly sent to the Marion County Children's Guardian Home. After his mother escaped, Burton's father went to jail for two years. Burton's mother remarried, and Burton and his younger brother and sister had happier teenage years.
Burton worked as a caddy at a local country club in order to make ends meet, where he learned the golf skills that led to his winning a statewide golf championship in high school. He graduated from Shortridge High School in 1957, and attended Indiana University (1958–59) and the Cincinnati Bible Seminary (now known as Cincinnati Christian University) (1959–60). He served in the United States Army from 1956 to 1957, before leaving active duty to return to college but remained in the Army Reserves from 1957 to 1962. After school, Burton became a real estate broker and he founded the Dan Burton Insurance Agency in 1968.
Burton first ran for Congress in 1970, losing to Democratic incumbent Andy Jacobs in Indiana's 11th congressional district. Burton ran again in 1972, losing in the Republican primary to William Hudnut.
After the 1980 census, the Republican-controlled state legislature reconfigured the 6th District into a heavily Republican district focused on the suburbs north of Indianapolis. The district's four-term Democratic incumbent, David W. Evans, opted to challenge Jacobs in the Democratic primary (which he lost) rather than face certain defeat. Burton jumped into the Republican primary halfway into his second stint in the state senate, and won a five-way Republican primary with 37% of the vote. He then defeated Democrat George Grabianowski in the general election 65%–35%. He would be reelected 14 times, never dropping below 62% in a general election. His district was renumbered as the 5th District after the 2000 census.