From 1975 to 1981, Collins coached at Southern Miss, and compiled a 48–30–2 record. In 1982 he was hired by SMU, signing a five-year deal with more than $100,000 annual salary. While at SMU, Collins compiled a 43–14–1 record. His only losing season as a coach came in 1976, when he went 3–8 at Southern MIss. From 1982 to 1984, he put together the best stretch in SMU's history, going 31–4–1.
After the season, Collins, athletic director Bob Hitch and recruiting coordinator Henry Lee Parker were interviewed by WFAA-TV's Dale Hansen regarding allegations that players were being paid. Collins denied any knowledge of the affair. It later emerged that Collins knew that players were being paid, though he didn't know who they were. Collins resigned shortly after WFAA aired a special report breaking the scandal, and was later given $850,000 in severance pay in return for keeping quiet about the payments.
Collins was not sanctioned by the NCAA for any role in the events leading up to the "death penalty," though the final report criticized him for not providing a convincing explanation for why players were still being paid after the school assured the NCAA that the payments had stopped. Nonetheless, his reputation was ruined. While he was a finalist for the open head coach's job at Mississippi State in 1990 (which eventually went to Jackie Sherrill), he has never returned to the collegiate ranks in any capacity since leaving SMU.