"There's not much you can do," Weber said. "We thought if we were solid sooner or later we'd wear them down and they'd start missing them, but obviously they didn't tonight."
For that reason, the Wildcats (8-2) could never shake the Tigers (1-10), who trailed by just six points with 1:13 remaining. But four free throws in the final 35 seconds protected Kansas State's lead.
Penn had 24 points for Texas Southern, and Omar Strong and Madarious Gibbs added 13 points each.
A 7-0 run by the Wildcats — five of the points were by McGruder — gave them a 46-36 lead with 15:03 remaining. It was the first double-digit advantage of the game.
The lead grew to 53-38 with 12 minutes to play. But Texas Southern went on a 10-2 spurt that included 3-pointers by Penn and Gibbs.
With 7:40 left, Texas Southern trailed 55-48 and hung in until the final minutes.
Kansas State shot 56.4 percent (31 of 55) from the floor.
Texas Southern's success from behind the arc kept the game close early. The Tigers converted five of their first nine 3-point attempts and scored 18 of its 31 first-half points on 3s.
Kansas State went 1 for 7 from 3-point range in the opening half. The Wildcats led just 35-31 at the break and needed a 15-5 run toward the end of the half to get there.