Gary Flowers scored 14 points and R.L. Horton had 12 for the Golden Eagles (20-12), who will play No. 7 seed Houston in the semifinals Friday. Houston knocked off No. 2 seed Memphis earlier in the day.
"I've had some great teams but I don't know that I've ever had a team overcome adversity," Southern Miss coach Larry Eustachy said. "We've got a lot of work to do here, but it's a good start. It's a good start, and we're 80 minutes away from going to the NCAA tournament."
Jamarr Sanders scored 10 points to lead the Blazers (23-8), who fell behind 16-2 in the first five minutes and never recovered.
UAB swept the regular season series between the teams, but it was a different result this time. The win also snapped a five-game losing streak for Southern Miss against the Blazers.
"It feels awesome," Horton said. "We always get right there and can't seem to get over that hump. This year the ball has started bouncing our way a little bit."
UAB, which was ranked in the Top 25 earlier this season, shot only 39.1 percent from the field and made only 4-of-15 free throws.
Southern Miss was worse from the field, shooting 33.3 percent, but hit 25-of-30 free throws and outrebounded the Blazers 34-27.
"I thought we were doomed from the start," UAB coach Mike Davis said. "There was no fight."
UAB went on a 9-0 run in the second half, cutting the deficit to 34-26. But the Eagles answered with consecutive 3-pointers from Horton for a 14-point cushion with 14:38 left.
UAB later drew to within 48-39, but Southern Miss scored the next nine points for its largest lead, 57-39 with 1:40 remaining.
"We jogged down the court on defense," Davis said. "We never blocked out. We gave secondary chances from rebounds. We didn't get into our offense the way we were supposed to. We played soft. They played discipline. Every guy we put in got softer and softer."