McNair was initially offered a full scholarship to the University of Florida to play running back, but, wanting to play quarterback, McNair chose Alcorn State University, a Historically Black University which competes in the NCAA's Division I-AA (now known as the Football Championship Subdivision) Southwestern Athletic Conference (SWAC). In 1992, McNair threw for 3,541 yards and 29 touchdowns, and ran in for 10 more scores. The Braves fashioned a record of 7–4, including a last-second victory in their rematch with Grambling. In that contest, McNair returned from an injury and helped Alcorn State, trailing late in the final period, move deep into Tigers' territory. Then, despite a leg injury, he tucked the ball under his arm and dove into the end zone for the winning touchdown. The victory over Grambling helped the Braves qualify for the I-AA playoffs where they faced off against then-Northeast Louisiana, falling 78–27 to the Indians on November 21, 1992. McNair helped Alcorn State to another good year in 1993, as the Braves upped their record to 8–3 while McNair threw for more than 3,000 yards and 30 touchdowns. He was also named First-Team All-SWAC for the third year in a row.