Texas (33-10, 15-5 Big 12) has either won or swept every series against OU (30-13, 9-9 Big 12) since 1998 and has won 10 straight games against its conference rival.
The Sooners got out to a hot start by scoring all three of their runs in the second inning, but one good inning was all their bats would put together in the loss.
Then Texas senior pitcher Cole Green settled down and took control.
He allowed just two runners to reach base after the second inning until he was pulled from the game to start the seventh.
Green, last year's Big 12 Pitcher of the Year, gave up the three runs on three hits and struck out six in six innings.
While Green shut down OU's bats, Texas' offense heated up enough to take the lead.
Junior pitcher Burch Smith gave up a solo homer to freshman third baseman Erich Weiss in the second and four straight singles to start the bottom of the third. Those four singles resulted in three runs and the end of Smith's day.
He gave up four runs on five hits in 2 1/3 innings before redshirt freshman lefty Jordan John took over.
John did give up the double to senior center fielder Paul Montalbano that brought in the game-winning run, which was credited to Smith, but the reliever didn't allow more than one runner to reach base at a given time in his 5 2/3 innings.
John gave up three hits and struck out three batters.
The Sooners got the tying and go-ahead runs on base in the bottom of the ninth with two outs, but junior designated hitter Evan Mistich's well-hit line drive went directly to the right fielder to end the game.
OU will try to avoid the sweep at 1 p.m. Sunday. If it can't, then the loss would mark the Longhorns' third straight season sweep against the Sooners.