Hance was born in Dimmitt in Castro County, Texas, on November 14, 1942. He attended Texas Tech University in Lubbock and went to law school at the University of Texas at Austin. After law school, he was admitted to the Texas bar and became a practicing lawyer in Lubbock in 1968; during this period, he was also a professor at Texas Tech from 1968 to 1973.

Hance served in the Texas State Senate from 1974 to 1978, when he ran successfully as a Democrat for the U.S. House. The seat had been held for a generation by popular Democrat George H. Mahon, long-time chairman of the House Appropriations Committee. Hance's opponent in the general election was a young Republican from Midland, George W. Bush. Hance portrayed Bush as "not a real Texan" because of his privileged upbringing and Yale education, in contrast to the image that Bush would later develop. Hance later said in an interview that for Bush, the lesson was that "he wasn't going to be out-Christianed or out-good-old-boyed again." Hance is the only person ever to defeat George W. Bush in a general election.

Hance was reelected two more times. Like Mahon, he wore his party ties very loosely, compiling a very conservative voting record even by Texas Democratic standards. He did not run for a fourth term in 1984, instead opting to seek the Democratic nomination for the Senate seat being vacated by the retiring Republican John G. Tower. He was defeated by the most liberal candidate in the race, State Senator Lloyd Doggett of Austin, who was later a long-term Democratic congressman. Hance's House seat was taken over by a young Republican Larry Combest, a former aide to Senator Tower. Combest served until his resignation in 2003. The seat had become increasingly friendly to Republicans over the years, and has remained in Republican hands ever since Hance left the House.

Hance himself became a Republican in 1985. In 1986, he unsuccessfully sought the Republican gubernatorial nomination. Party voters instead called former Governor Bill Clements out of retirement for the right to challenge Democratic Governor Mark White. Clements defeated White in the general election and served a second nonconsecutive four-year term. In 1988, Hance was a Texas delegate to his first ever Republican National Convention, which met in New Orleans.

In 1987, Clements appointed his former intraparty rival Hance to a vacancy on the Texas Railroad Commission. Hance was elected as a Republican to the commission on the coattails of presidential nominee George H.W. Bush, father of the young man Hance had defeated for Congress ten years earlier. He left the Railroad Commission in 1990, one again to seek the GOP nomination for governor but lost out to Midland businessman Clayton Williams, Jr., who in turn was narrowly defeated in the November general election by the Democrat Ann Richards. In 2004, against the wishes of Governor Rick Perry, Hance assisted Supreme Court Justice Steven Wayne Smith in the latter's unsuccessful bid for renomination.