The Horned Frogs (6-2) were aided by Abron's performance in the second half, which included 13 points and four rebounds, and helped TCU regain the lead and pull away from the Thunderbirds.
The Horned Frogs led 31-28 at halftime. Southern Utah (1-5) grabbed a 38-37 lead when Damon Heuir made two free throws with 10:49 to play. Abron's layup put TCU back in front and they stayed there the rest of the way.
It was still a five-point game after Jayson Cheesman's tip-in for Southern Utah with 1:59 left, but Anderson's layup extended TCU's lead to 54-47.
Heuir led all scorers with 25 points on 7-of-14 shooting. Cheesman had 13 rebounds. Southern Utah shot 27 percent in the second half and 33 percent overall.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.