Prairie View (7-15, 5-5 Southwest Athletic Conference) shot 53 percent from the floor and made 8 of 18 beyond the arc. John Brisco chipped in with 16 points.
The teams were tied at 38 with 2:25 left in the first half after a 3-pointer by Chapman. The Panthers then closed the half on a 9-3 run to lead 47-41 at the break.
Prairie View was able to hold off Texas Southern in the second half by making 4 of 7 3-pointers and 12 of 17 from the line.