The Bearkats totaled only four hits but three of the four produced RBIs. The Mavericks produced six hits.
UTA struck first as Courtney Enocksen brought in a run with a second inning single.
First baseman Kim Damian scored two runs with a double then center fielder Tori Benavidez blasted a two-run homer to put Sam Houston up 4-1 in the top of the third inning.
The Mavericks got run one back in the bottom of the third on a sacrifice fly by Erica LeFlore.
Second baseman Alyssa Coggins added two more runs with a single in the top of the seventh.
Tomi Garrison picked up the win in the pitching circle, spreading six hits over seven innings while striking out two batters.
Sam Houston stands in second place in the Southland race and now has won 24 of its last 28 games (since starting the year 1-13) to stand 24-17 on the year.
The Bearkats and the Mavericks play the second game of the series Saturday at 2 p.m.