The second-seeded Tigers (15-17) will face top-seeded MVSU or fifth-seeded Arkansas-Pine Bluff for the championship Saturday night.
Madarious Gibbs added 12 points and D'Angelo Scott 10 for Texas Southern, which shot only 33 percent (17 of 52). Daniel King's 10 rebounds helped the Tigers forge a 42-33 edge on the boards.
Ken McDonald and Anthony Nieves led the sixth-seeded Braves (10-22) with 11 points apiece. Martrevious Sanders had 10 points and eight assists, and Michael Starks blocked four shots.
An 8-1 run put Texas Southern ahead 37-33 with 16:40 left. The Tigers did not trail again, though their lead never stretched beyond seven.
Alcorn State closed within 55-51, but the Tigers went 5 of 6 from the line in the final minute.