As a sophomore, he was moved from outside linebacker to defensive end, becoming a starter midway through the season and finishing with a team-best 12 sacks.
He earned second-team All-American honors for a Hurricanes team that finished was narrowly defeated at the 1987 Fiesta Bowl by Penn State 14–10 for the National Championship.
Noted as a defensive stalwart as a senior in 1987, opposing offenses tried to steer plays away from Stubbs direction, but he still posted 75 tackles and 9.5 sacks and helped the team win their second National Championship.
In the Super Bowl XXIV victory over the Denver Broncos, he had 2 sacks and returned a fumble recovery to the one-yard line to set up a 49ers touchdown.
[6] On April 7, 1995, he was signed as a free agent by the Philadelphia Eagles, reuniting him with Ray Rhodes, a former defensive assistant with the 49ers.
On April 4, 1996, he rejected an offer from the Eagles and signed instead a one-year contract with the Miami Dolphins,[8] reuniting with Jimmy Johnson.
[11] The Stubbs Sandwich is a food item named in his honor, that is sold in a restaurant chain in Coppell, Texas and heavily endorsed by John Madden.