"The game is never over when you play us," Houston coach Todd Whitting said. "I'm proud the way they battled late. We had to make a lot of moves at the end and everybody we put in the game did their job."
Hinojosa' ninth-inning catch delivered the win for Texas starter Parker French (2-1). Nathan Thornhill, who relieved John Curtiss in the ninth, only faced Vidales to get his second save.
Houston took a 1-0 lead in the second inning on Landon Appling's infield single, scoring Casey Grayson, who had two hits and led off the second with a deep double to left-center. Texas scored a run in the second inning and two in the third off hard-luck Houston starter Jake Lemoine (1-1), who allowed only one earned run and three hits in seven innings.
Houston out-hit Texas 9-4, with Hinojosa getting two hits. But the Longhorns made the plays they needed, and took advantage of the Cougars' lapses in the field.
Texas (8-3) is 2-0 in the Houston College Classic and meets Sam Houston State, who is the only other 2-0 team, on Sunday at 10:05 a.m. CT in the final day of the six-team, nine-game classic.
Texas coach Augie Garrido said winning Friday and Saturday was huge, especially handing Houston its first loss.
"It's very big," said Garrido. "Anytime you can win, especially against an opponent like this that's been playing well, and their teams is well structured, they're a good-looking team.
"It's important that every win we get, and the closer they are like this, is more important because it's relating to mental toughness, which is what we've been preaching."
In the Houston ninth, pinch-runner Cole Coakley scored on Jacob Lueneburg's fielder's choice off Curtiss.
French scattered seven hits in seven innings, allowing one run and one walk. The junior right-hander struck out seven and got 10 outs on grounders.
"He was probably as good as he's ever been," said Garrido. "He's got that slider now that gives him another weapon and it keeps them more off balance when he threw sinker after sinker. And he's mixing in the changeup."