Serena Hines crossed the ball from the right wing to Brown at the far post to set up the winning goal at the 84:46 mark.
Texas State totaled 17 shots while Sam Houston took 11. Bearkat goalkeeper Kyle Hambleton saved seven shots while Bobcat keeper Natalie Gardini was credited with four saves.
Eleven of the Bobcats' shots came in the second period while Sam Houston was limited to six attempts in the final 45 minutes.
Ashley Alonzo, the freshman forward who scored the match-winner for Sam Houston in the Kats' 1-0 season-opening victory over Prairie View Friday, led the SHSU offense with four shots. Shelby McDaniel and Tricia Mallory each had two shots.
The match was the season opener for Texas State. Sam Houston is 1-1 for the year. The Bearkats' next opponent is North Texas Friday at 7 p.m. at Intramural Field three.