Baylor (14-5, 5-1 Big 12) won its third in a row and is off to its best start in conference since 1997-98.
Austin sprained his right ankle on the final play before halftime before returning early in the second half. The 7-foot-1 freshman had two dunks in an 18-2 run in the first half that gave the Bears a 41-17 lead.
Adrick McKinney scored 15 points and Connell Crossland chipped with 12 for TCU (9-11, 0-7)
The Horned Frogs, who are in their first season in Big 12, are 0-7 in conference play for the first time since 1978-79. The school was in the now defunct Southwest Conference at the time.