Swing had a team-high nine rebounds and was 7 of 13 from the field for the game. Rod Rucker had 11 points.
UAB was up 32-23 at halftime and led until Brian Bernardi hit two free throws to put the Mustangs up 52-51 with 29 seconds remaining. Swing’s layup put the Blazers (16-16) back on top. No. 10 seed SMU missed a jumper with a second to play.
No. 7 seed UAB will play No. 2 seed Southern Mississippi on Thursday in the quarterfinals.
Head coach Larry Brown, who is the only coach to win an NCAA and NBA title, ends his first season at SMU.