Jackson was known as "the other end" at the University of Pittsburgh due to Hugh Green's presence on the team. He also played with other future NFL players, such as center Russ Grimm, guard Mark May, tackle Jimbo Covert, defensive back Tim Lewis, defensive lineman Bill Maas, receiver Dwight Collins, and quarterback Dan Marino. Although overshadowed by Green, as a junior in 1979 Jackson was a second-team All-East selection and named an honorable mention All-American by the Associated Press and The Sporting News. As a senior in 1980, he was a second-team All-America selection and a first-team All-Big East selection. Pitt's defense was ranked number one nationally in 1980.
Jackson ended his college career with 290 tackles, 166 of them unassisted. He also finished with 21 sacks, four passes defended and three interceptions. As a freshman, he totaled 15 tackles and two interceptions, one returned for a touchdown. As a sophomore, he made 27 tackles (21 unassisted) and five sacks. In 1979, he had 111 tackles (47 unassisted) and four sacks and recovered two fumbles. In 1980, he led the team with 137 tackles (87 solo), had 12 sacks, broke up four passes, recovered four fumbles and intercepted a pass. Following the game against Army in 1980, in which Jackson recorded 12 tackles, three sacks, a forced fumble, an interception, and a blocked punt, he was named the Sports Illustrated Player of the Week. That same year, during the game against Penn State, he was chosen the ABC/Chevrolet Player-of-the-Game.