Donnie Joseph (2-1) earned the victory, allowing one run on a hit and a walk while striking out two in two innings of relief. Brad Mincey took the loss, giving up a run on a pair of hits and failing to get an out.
Houston (35-21) advances to play the winner of the Rice-UAB game. East Carolina (39-18) will play the loser of the Owls-Blazers match in an elimination game.
The Cougars overcame a pair of potentially costly plays. With the score tied at 3 in the bottom of the ninth, pinch runner Felix Fanaselle was picked off second base with one out. Then, with two outs in the top of the 10th, left fielder Jake Stewart misplayed a fly ball that turned into Henderson's double.