The Horns went hitless for four frames but took a 1-0 lead in the top of the fifth after Scott Dodge opened the inning with a single. Dodge advanced to second on a wild pitch and moved to third on a sacrifice bunt and scored on Taylor Teagarden's sac fly.
The Owls loaded the bases with two outs in the seventh but reliever Huston Street got Jeff Jorgensen to ground out to second to end the inning. But Rice knotted the affair with an Enrique Cruz solo home run in the bottom of the eighth off of the UT closer.
Texas threatened in the top of the 10th with men on first and second with two down but could not advance the runners. The Owl defensive stand set up Kolkhorst's game-winning double down the right-field line.
Texas opens its Big 12 slate when it returns home to Disch-Falk Field for a three-game series against Missouri starting at 6:30 p.m. Friday.