Born and raised in the small town of Panguitch, Utah, Owens graduated from Panguitch High School in 1955, then attended the University of Utah in Salt Lake City, from which he earned his Bachelor's degree in 1961 and his Juris Doctorate in 1964. Owens' undergraduate education was interrupted while he served as missionary to France for the Church of Jesus Christ of Latter Day Saints (Mormon Church) from 1957 to 1960. In France, he met his future wife, Marlene, a fellow missionary for the church. Owens reportedly worked his way through college and law school by washing dishes at the Bryce Canyon Café. He then worked as a lawyer in private practice and as a staffer for three United States Senators, Frank Moss of Utah, Robert F. Kennedy of New York, and Edward M. Kennedy of Massachusetts. He was the Western states coordinator for the presidential campaigns of Robert Kennedy in 1968 and Edward Kennedy in 1980, and served as a delegate to the Democratic National Convention in 1968 and 1980.

In 1972 he was elected to the US House of Representatives as a Democrat by "walking for Congress" throughout the district to meet voters personally. He ran an unsuccessful Senate campaign against Jake Garn in 1974, then served as a mission president of the LDS Montreal, Canada, Mission from 1975 to 1978, after which he returned to Salt Lake City to practice law. In 1984 Owens lost the Utah gubernatorial race to Republican Norm Bangerter but was re-elected to the House in 1986 and served through 1992, when he ran another unsuccessful Senate campaign, this time losing to Bob Bennett. Following his Senate defeat, he retired to semi-private life but remained a tireless proponent for the causes he had championed in Congress.

Throughout his congressional career, Owens was a friend to environmentalists (he would later serve on the boards of several environmental organizations within the state), an advocate for “downwinders” who had suffered radiation exposure during atomic testing in Nevada in the 1950s, a strong supporter of the Central Utah Project to bring much-needed water to the region, and founder of the Center for Middle East Peace and Economic Cooperation. He always considered his vote, along with the votes of his fellow freshman congressmen, to force the vote that ended the Vietnam War to be one of the highlights of his career.

On December 18, 2002, Owens suffered a heart attack in Tel Aviv, Israel while on a trip to further the cause of Middle East peace and died. Conspiracy theories claim that he was murdered because of his work on the Middle East Center for Peace but no evidence substantiates this claim.

Preceded by: Sherman P. Lloyd U.S. Congressman, Utah 2nd District 1973 - 1975 Succeeded by: Allan Turner Howe

Preceded by: David Smith Monson U.S. Congressman, Utah 2nd District 1987 - 1993 Succeeded by: Karen Shepherd