Stein's third field goal in the third quarter put the Golden Eagles (6-3, 4-1 Conference USA) on top 23-2 before Jack Abraham had a pair of touchdown passes, 20 yards to Quez Watkins and 9 to Tim Jones.
Abraham was 17 of 22 for 164 yards and with Kevin Perkins picking up 94 yards on just six carries, Southern Mississippi piled up 325 total yards. UAB was leading the league in allowing just 255 yards, 92 on the ground.
A first-quarter interception by Shannon Showers led to a 6-yard touchdown run Steve Anderson in the first quarter. Thomas followed up Stein's first field goal with his pick-6 early in the second. Stein kicked a 44-yard field goal on the last play of the first half for a 20-2 lead.
UAB (6-3, 3-2) only had 173 yards on offense.
It was the 600th win in 103 years of football for Southern Mississippi.
Justin Herbert helps draft cause with MVP showing at Senior Bowl
Justin Herbert completed 9 of 12 passes for 83 yards with one TD and no interceptions en route to being named MVP of Saturday's Senior Bowl. He also earned "Practice Player of the Week" honors.
Notre Dame releases CB Landen Bartleson from letter of intent after arrest
Notre Dame has released 2020 cornerback signee Landen Bartleson from his national letter of intent after he was arrested in connection with a gun store robbery in Danville, Kentucky.
Kiper doesn't see Young surpassing Burrow for No.1 pick
Mel Kiper Jr. doesn't see any way the Bengals take Chase Young over Joe Burrow with the No. 1 overall draft pick.
Former ACC commissioner Gene Corrigan dies at 91
Former NCAA president Gene Corrigan, who served as ACC commissioner from 1987 to 1996 and engineered the addition of Florida State as the conference's ninth member in 1990, has died at the age of 91.
Larry Fedora named Baylor's offensive coordinator and quarterbacks coach
Larry Fedora, who previously was the head coach at Southern Miss and North Carolina, was named Baylor's offensive coordinator and quarterbacks coach on Saturday.
USC hires Todd Orlando as DC to replace Clancy Pendergast
Todd Orlando has been hired as USC's new defensive coordinator, the school announced Friday.