Julien Lewis scored 16 points and Sheldon McClellan had 13 for the Longhorns (7-5), who couldn't match the efficiency of their 85-67 win over North Carolina on Wednesday night.
Texas trailed 41-40 and had a chance to take a lead, but McClellan missed two free throws after a technical on Nix. The Spartans promptly grabbed a three-point lead on a jumper by Payne. They later made it 49-40 on two free throws by Nix and Appling's 3-pointer.
It was 54-44 when the Longhorns cut the lead in half. A three-point play by Ioannis Papapetrou made it a four-point game, and his jumper as the shot clock expired cut the margin to 56-54. After Payne and Appling built the lead back to six and Texas' Jonathan Holmes was called for charging, Nix added a free throw to build the lead back to seven.
Nix fittingly grabbed the game's last rebound, giving his team a 36-32 edge on the boards. That and 17 second-half free throws helped immensely.