Baylor had a 16-point lead erased just after halftime, but the Bears pulled away with a 13-2 run in the second half.
Austin was 11 of 19 from the field. Cory Jefferson added 10 points for Baylor (6-3), which snapped a two-game home losing streak.
Baylor led 35-19 in the first half before Lamar came back to tie it early in the second. Trailing 38-31 at halftime, Lamar outscored Baylor 11-4 to open the second half. Amos Wilson and Donley Minor had consecutive baskets to tie the game at 42 with 17 minutes remaining.
Baylor was up 58-55 before going on its 13-2 spurt.