Damian singled in the third inning and doubled in the sixth.
Bearkat pitcher Tomi Garrison pitched all six innings, facing 28 batters, giving up eight hits and striking out on batter.
Texas scored one run in the first inning but picked up three more in the third on RBI singles by Courtney Craig, Taylor Thorn and Lexy Bennett. The Longhorns picked up another run in the bottom of the sixth inning.
Blaire Luna was the winning pitcher for the Longhorns.
Sam Houston and Texas will meet in single games Saturday and Sunday afternoon.