Evans was born in Hobbs, New Mexico, the son of Gladys, a home cleaner, and Oscar, a preacher and janitor. Robert was the fourth of seven children, all of whom would go on to graduate college. Evans played high school basketball at Hobbs High School under legendary coach Ralph Tasker. His senior year he was named co-captain. That year the team made it to the 1964 championship game and Evans was invited to the state all-star game in Albuquerque. Evans played junior college basketball at what is now Lubbock Christian University where he was named the school's first All-American. Both seasons he played at Lubbock Christian Evans was voted the teams’ best defensive player. In his second year with the team Evans was named team captain. In 1966 Evans earned his associate degree in Arts and Sciences. At Lubbock Christian Evans was teammates with Gerald Turner who would later become Chancellor of the University of Mississippi. Turner was instrumental in Evans’ hiring as head basketball coach in 1992. Evans transferred to New Mexico State University for the 1966–67 season where he was coached by Lou Henson. He was named team captain and led the Aggies to a 15–11 record and a NCAA Tournament appearance. The next season Evans again captained the team to a 23–6 record and another NCAA Tournament appearance. In 1967 Evans was selected NMSU's most outstanding athlete. In May 1968 Evans earned his bachelor's degree in education.
Coaching career
After his graduation, Evans was hired as an assistant at New Mexico State under Henson. When Henson left for Illinois in 1976, Evans moved to Texas Tech and served for 14 years as an assistant under Gerald Myers. After two years as an assistant at Oklahoma State under Eddie Sutton, Evans was hired at Ole Miss as its first black coach in a major sport. Evans inherited a program that had been one of the dregs of the Southeastern Conference for decades. The Rebels had not had a winning season in SEC play since 1982–83, and had only finished in the top half of the conference twice in 59 years of conference play. After four years rebuilding the program, the Rebels shocked the SEC by winning consecutive West Division titles in 1997 and 1998 and notching the first 20-win seasons in school history. Ole Miss had been one of the few longstanding members of a "power conference" to have never won 20 games in a season. In 1998, Evans moved to Arizona State, which was reeling in the wake of a point-shaving scandal. His tenure at Arizona State was not nearly as successful as his tenure at Ole Miss, with only one NCAA appearance in eight seasons He was fired after the 2006 season.