After Shelton's three-point play with 21 seconds left tied it at 83, TCU had one more chance. But Thorns missed on a drive when his bank shot ricocheted off the rim and Shelton came down with the rebound.
San Diego State has won 14 of its last 15 overtime games.
The Aztecs ended the regular season by winning their last four games. That came after the program's first three-game losing streak in more than four years, which included a home loss to New Mexico after having beaten the Lobos on their home court in mid-January.
A buzzer-beating layup by DeShawn Stephens at the end of the first half put San Diego State up 46-34. That capped a 10-2 run over the final 2:01 of the first half, and the Aztecs added to that with two baskets in the first 44 seconds after halftime.
"This was a tough game, and a hard-fought game. I knew, our coaches knew, I'm not sure our players knew," Fisher said. "When we hit the first two baskets in the second half and we were up 16, they took a timeout. They weren't going to go away. I've watched enough."
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