TCU (5-3) won for the fifth time in six games, jumping out to a 34-22 lead by halftime. The Horned Frogs led by 18 early in the second half, but the Bulldogs pulled within 59-56 on Roquez Johnson's putback with 2:24 remaining.
It was the closest they would get. The Horned Frogs scored the next four points and made the most of their free throws down the stretch to seal the win.
Mississippi State (5-2) lost for the first time at home this season. Craig Sword led the Bulldogs with 24 points on 9 of 12 shooting from the field.
TCU made 25 of 31 (80.6 percent) free throws and 6 of 14 (43 percent) from 3-point range.
Jarvis Ray scored TCU's first two points on a pair of free throws with his shorts on backward.
He was then summoned to the bench, laughing as he made the wardrobe adjustment while a pair of teammates shielded him from the crowd. It was one of the few mistakes by the Horned Frogs in the first half.
TCU led after the first minute and pushed ahead 19-8 by midway through the first half thanks to nine straight points by Hill.
The 6-foot-2 sophomore came off to bench to score 10 points in the first half as the Horned Frogs pushed out to a 34-22 halftime lead. Mississippi State shot just 9 of 25 from the field (36 percent) in the first half and missed all six of its 3-point attempts.
But Mississippi State methodically fought back in the second half, using a few big 3-pointers by I.J. Ready to vault back into the game. Ready, a freshman guard, was playing his first game after missing three weeks with a strained hamstring. He finished with nine points.
Mississippi State escaped with a few wins last week, pulling out close games against Jackson State and Loyola despite not playing particularly well.
But the Horned Frogs weren't nearly as forgiving and punished the Bulldogs' defensive lapses, slicing through the lane for easy baskets.
It was TCU's first game since the loss of starting forward Amric Fields, who broke his hand in last week's loss to Harvard.