Behind a season-high four home runs, including a grand slam by Matesich, the Golden Eagles improved to 29-13 overall and 7-6 in C-USA play.
Houston, which used four pitchers that combined for six walks and five hit batters, dropped to 26-15 and 8-5 in conference play.
Dating back to the 2006 season, Southern Miss has won four straight against the Cougars. The Golden Eagles have also won four consecutive games since losing at Tulane last Saturday behind 45 runs scored and 10 home runs.
"We are swinging the bat well," Southern Miss coach Corky Palmer said. "We got 12 runs off 10 hits - hitting home runs has been big since Tulane last Sunday.
"It was a big win."
The Golden Eagles had to rally from a 3-0 deficit, after going hitless through 32/3 innings against Houston starter Wes Musick.
Houston scored its three runs in the third inning off Billeaud when Ryan Lormand cleared the bases with a double to left center. The three base runners came off two walks and a shallow single to center by Bryan Pounds.
Then Billeaud, a junior, retired the next 11 Cougars, including three via strikeout, before allowing an infield single to Blake Kelso with one out in the seventh and Southern Miss leading 12-3.
The Golden Eagles finally got to Musick (7-3) in the bottom of the fourth with four earned runs, including a solo home run by Keith Winstead, his second of the season, and a two-run shot by Bo Davis, his third.
After Billeaud retired the side in the fifth with a flyout and two strikeouts, Southern Miss stretched its lead to 6-3.
Trey Cuevas followed with a double to left off Musick before Winstead was hit by a pitch. After Michael Ewing put the runners in scoring position with a sacrifice bunt, Matesich scored Cuevas on a sacrifice fly.
Drew Carson then singled to center to score Winstead for a 6-3 lead.
"Musick is one of the top five pitchers in the league," Palmer said. "They staked him to a 3-0 lead and we caught him. That was big."
Billeaud, coming off losses to LSU and Tulane, retired the side again in the sixth with two groundouts and a flyout.
With the bases loaded in the sixth after two walks and a hit batter, Matesich greeted Taylor Hammack, the third reliever of the night, with a first-pitch grand slam. Kyle Maxie closed out the scoring with his fifth home run of the season to give Southern Miss a 12-3 lead.
"I knew I hit the ball deep enough to get a sacrifice," Matesich said. "I didn't think I hit it enough to get the ball out."
Houston added a pair of runs in the seventh and four in eighth inning to trim the lead to 12-9.
Billeaud, now 3-3, allowed five runs in 61/3 innings of work and threw 119 pitches.