Melton's two-run homer off Houston starter Jake Lemoine in the fourth inning was his second of the season and started the scoring. Barash opened the top of the fifth with his first homer of the season, giving the Aggies a 3-0 lead.
The Aggies (15-0) broke the game open with a three-run seventh inning. All three runs were unearned after an early fielding error. The inning was highlighted by a triple from Ryne Birk and a double from Barash.
"Grayson was Grayson," said Barash. "That's what we expect from Grayson every weekend.
"That's what he does. He keeps the ball down on the ground."
Josh Vidales, Justin Montemayor and Michael Wisz collected the only hits for Houston (8-7), all singles.
Richard Dean is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.