Last season, UH advanced to the College Station regional final, but fell to Texas A&M.
The Cougars, seeded No. 8 nationally, will play host to either Lousiana-Lafayette or LSU next weekend at Cougar Softball Stadium. Game dates and times for the best-of-3 series will be announced later Sunday night.
The winner of the Super Regional will advance to the 2008 Women's College World Series, set to take place from May 28-June 4 at ASA Hall of Fame Stadium in Oklahoma City.
The Cougars were led by junior Haley Valis, whose 10th home run, a solo shot over the center field fence in the fifth inning, put Houston on the board first. Valis became the fourth Cougar to reach double-digit home runs this season.
Houston loaded the bases in the sixth inning and junior Katie Bush scored the Cougars second run after a walk by junior Laurie Wagner.
The Huskies avoided a shutout when Morgan Stuart hit a home run over center field in the top of the seventh inning.
Angel Shamblin (35-3) pitched a complete game. She allowed two hits and one run, while striking out seven.
In three Regional contests, Shamblin went 3-0, giving up three hits and one run while notching 23 strikeouts with a 0.37 ERA.
NCAA super regional all-session tickets can be purchased at the ticket office in the Athletic Alumni Center or online at UHCougars.com.