Tolliver struggled at the start of the year; by the end of September he had only completed 54 of 123 passes. After throwing five interceptions in a game against Baylor, he shrugged off the bad game, saying, "even Betty Crocker burns a cake every now and then." His fortunes continued to sink when in a game in late October against the Rice Owls, he was benched, and backup quarterback Monte McGuire rallied the team to a victory. However, Tolliver regained his starting job and brought his team to the 1986 Independence Bowl as Texas Tech won six games for the first time since 1978. He finished the season with 1,802 passing yards and seven touchdowns. Tolliver began his junior year facing Florida State, a game in which he suffered a hairline fracture in his foot, leaving him doubtful for the match. He missed the first three games of the season but returned in Texas Tech's fourth game against Baylor, completing 14 of 25 passes for 189 yards, a touchdown and an interception in a 36–22 loss. Tolliver's next big performance came against TCU, the same team he defeated 63–7 as a freshman. He threw a touchdown pass to Wayne Walker in the last minute to beat TCU 36–35. He finished the season having passed for 1,422 yards and seven touchdowns in eight games. The next season, his senior year, Tolliver and Texas Tech sought to win the Southwest Conference. He started the season strong, throwing an 85-yard pass against Arizona—it was the third-longest pass in school history—but the Red Raiders started with two losses. By the end of the season, Tolliver had set 16 school records and was awarded the Southwest Conference Sportsmanship Award by the league's officials. After four seasons with Texas Tech, he set the school record for career passing yards (6,756), career pass attempts (1,008), career pass completions (493), career touchdown passes (38), season passing yards in 1988 (2,869), and single game passing yards (446) against Oklahoma State University in 1988. Tolliver was inducted into Texas Tech's Hall of Honor in 2002. Tolliver was selected by the San Diego Chargers in the second round of the 1989 NFL Draft. The Chargers traded third, fourth, and seventh-round picks in exchange for the New York Giants' second-round pick in order to draft him. Tolliver was signed on July 31, 1989, after a short holdout. He was to compete with Mark Malone and David Archer for the starting job, a spot which eventually went to Jim McMahon after the Chargers traded for him.