Seniors Laurie Wagner and Amanda Grote and junior Haley Valis each hit home runs for the Cougars.
UH is now 8-2 in the all-time series against the Thundering Herd.
Coogs senior Angel Shamblin (14-1) pitched five innings, allowing two hits, one run, no walks and striking out five.
Houston will travel to Blacksburg, Va., to face No. 24 Virginia Tech on Tuesday. This will be the Cougars first ever matchup against the Hokies. Following Tuesday's game, Houston will play No. 19 Ohio State on Wednesday. UH is 0-1 all-time against the Buckeyes.
For more on the Coogs, go to www.UHCougars.com.