Ranked as high as No. 3 in the nation in preseason by Baseball America, Houston (9-7) snapped a four-game losing streak.
"In my five years here, this might have been the biggest win we've ever had," Houston coach Todd Whitting said. "We needed that one."
Houston was down 5-1 after five innings before tying it with a four-run sixth. Justin Montemayor knotted the score with a three-run triple. Houston scored three more runs in the next two innings to give the win to reliever Seth Romero (1-1), who did not allow an earned run in 5 1/3 innings.
"That's what I've been looking for, for about two weeks now, is a team that is resilient, plays with energy and doesn't stop," Whitting said. "Our veteran players stepped up."
Josh Vidales went 3-for-4 with three runs for the Cougars, who received two hits each from Jacob Campbell and Chris Iriart.
Matt Miller, who scored twice, had three of the 10 hits for Hawaii (6-10). JJ Kitaoka added two hits and two RBIs.
Richard Dean is a contributor to MLB.com This story was not subject to the approval of Major League Baseball or its clubs.