Alonzo launched a long ball from outside the box on the right wing that Panther Bianca Garza got a hand on, but couldn't control. The shot bounced into the left side of the net with 9:58 to play.
Sam Houston State dominated offensively, out-shooting the Panthers 18 to 8. But Prairie View (0-2) played tough defensively, frustrating the Bearkat attack at times.
"Prairie View did a great job of making it difficult," head coach Tom Brown said. "They put a lot of numbers behind the ball. I think we showed some early nerves but came back in the second half to overcome some frustration. We had a couple of chances in the second half that didn't go in but got a late goal for the victory."
Alonzo led the Bearkat attack with five shots. Two were saves. Shelby McDaniel fired three shots.
Senior goalkeeper Michelle McCullough picked up the shutout, making four saves.
Sam Houston State will play host to Texas State Sunday at 7 p.m. on Intramural Field 3 just west of Bowers Stadium.