Born in Colorado, Price grew up in Everett, Washington, north of Seattle. He was the son of Walt Price, the longtime head football coach at Everett Junior College. At Everett High School, Price was a teammate of the son of Pinky Erickson, the head coach at cross-town rival Cascade High. Everett High was coached by Bill Dunn, a next-door neighbor of the Ericksons. Dennis Erickson was a year behind Price, but took his job as starting quarterback midway through Price's senior year, and Price was moved to defense as a safety. The team finished 9–1. Price went on to play at Everett Junior College, Washington State, and finally at Puget Sound, where he co-captained the football team and was a member of the Phi Delta Thetafraternity. Price met his wife, the former Joyce Taylor, in kindergarten in the early 1950s. They were married at age 19 and they had three children: two sons and a daughter.
Following the 1980 season, Price landed his first head coaching position at Weber State of the Big Sky Conference, a job for which friend Dennis Erickson was also a finalist. Erickson would get the Idaho job the next year, and returned the favor by beating out Price for the Washington State job. Upon leaving just two years later for Miami, Erickson recommended Price, who got the WSU job and then rented Erickson's Pullman home. Price was at Weber State through 1988, compiling a record in eight seasons. His best year was 1987, when the Wildcats went 9–2, and advanced to the quarterfinals of the Division I-AA playoffs to finish at 10–3.
Washington State
On the field, Price was noted for his successful head coaching work at Washington State, where he served for fourteen seasons and compiled a record, with three ten-win seasons and five bowl appearances. His last two seasons at "Wazzu" combined for a 20–5 record. Price's 2002 team compiled a 7–1 mark in the conference and advanced to the Rose Bowl, where they were defeated by the Oklahoma Sooners 34–14. Five years earlier in 1997, Price was named National Coach of the Year, as the Cougars returned to the Rose Bowl after more than sixty years. During his tenure at Washington State, he mentored some of the greatest players in the school's history, including quarterbacks Drew Bledsoe, Ryan Leaf, and Jason Gesser. Prior to his departure, Price had recently signed a five-year contract at a base salary of $600,000 per year. With incentives, his compensation exceeded $900,000 in his final season at WSU. His original contract in 1989 was a four-year deal at $75,000 per year with unspecified television and radio revenues.
Price may be best known nationally for an off-the-field incident during his brief stint at Alabama. In December 2002, he was hired in principle to replace Dennis Franchione as the head coach of the Crimson Tide. Price was at Alabama during the 2003 spring practice, but in May his contract was rescinded shortly after news reports surfaced of Price being seen at a strip club during a trip to Pensacola, Florida, where Price was playing in a golf tournament, and he also had about $1,000 charged to his hotel room by an unknown woman staying in the room. This development came on the heels of an earlier reprimand for visiting campus-area bars and drinking into the early hours in Tuscaloosa.
UTEP
On December 21, 2003, Texas-El Paso announced the hiring of Price as its new head coach. At the press conference, Price said, "I feel reborn. I think this is the right situation for me. My dad told me a long time ago if you go somewhere where you're wanted and needed, your chances for success are a lot better. I want to be here. It's a match made in heaven." In his first season in 2004, he led the Miners to an 8–4 record and a berth in the Houston Bowl, where they lost to Colorado. It was a significant turnaround for the Miners, who had won only two games in each of their previous three seasons. UTEP earned its first-ever ranking in the AP Poll in 2004, rising as high as 23rd in early November. Price was a finalist for Eddie Robinson Award and the Paul "Bear" Bryant Award for coach of the year. His starting salary at UTEP in 2004 was $225,000 plus incentives. In 2010, Price became the second coach to take UTEP to three bowl games, after Mike Brumbelow, who led the Miners to the hometown Sun Bowl after the 1953, 1954, and 1956 seasons. Days before the final game of the 2012 season, Price announced his retirement. He returned as interim coach midway through the 2017 season following the departure of Sean Kugler, who had resigned after the fifth game; UTEP went winless for the season.