Omaha, Neb. Texas forgot all about its four losses to Big 12 Conference rival Baylor once the College World Series started.
"Once we get to Omaha, it's a brand new season," said Seth Johnston, whose two-run homer in the first inning provided all the offense Texas needed in a 5-1 victory over the Bears on Saturday night.
Instead of becoming the first Texas team to lose five times to an opponent in the same season, the Longhorns won for the 74th time in a record 32 appearances at the CWS, tying Southern California for most victories in Omaha.
Texas (52-16) advances to a Monday night game against Tulane, which defeated Oregon State, 3-1, early Saturday. Baylor (44-23) plays the Beavers in an elimination game Monday afternoon.
Adrian Alaniz pitched seven strong innings, and the Longhorns mixed Johnston's power with timely hits to beat a Baylor team that is at the CWS for the third time overall, but first since 1978.
"The balls they hit went to people and the balls we hit didn't," Texas coach Augie Garrido said. "It was good timing for the old Longhorns for that to happen."
Baylor swept a three-game series from the Longhorns in March, then beat them again last month at the Big 12 tournament.
In making it to the CWS for a fourth straight year, Texas has won their first game each time.
"Once you get to the park and you see Rosenblatt Stadium, you definitely remember you're in Omaha," Johnston said.
"Aside from that, it's almost felt like just another Big 12 Conference road trip."
Tulane 3, Oregon State 1
Scott Madden made sure the top-seeded Green Wave earned a first-round victory.
Madden delivered a two-out, two-run pinch-hit double in the seventh inning, sending Tulane to a victory over Oregon State and spoiling the Beavers' first CWS appearance since 1952. He is the only player left from Tulane's last trip to Omaha four years ago.
Tulane is attempting to become the first No. 1 national seed to win the CWS since Miami in 1999, when the NCAA expanded the tournament field to 64 teams.
Shut out for six innings by Jonah Nickerson and trailing 1-0, Tulane broke through for its 56th victory.
Winning pitcher Micah Owings started the rally with a leadoff single in the seventh.
The Beavers then nearly turned a double play on Mark Hamilton's bunt to third, getting a hard-sliding Owings at second, but the relay to first wasn't in time. Oregon State questioned the play, asking if there was interference on Owings' slide, but it was denied after the umpires huddled.
After a fly out, Brian Bogusevic singled to put runners at first and second.
Madden, who was a freshman on the Green Wave's 2001 CWS team and a starter as a catcher, then drove a 2-2 pitch to right center to put the Green Wave ahead. Madden received a medical redshirt in 2003 because of a bad ankle injury and earned his a degree last year before deciding to return this season.
Owings (12-4) allowed just four hits and a run in seven innings, throwing 123 pitches before being replaced by Daniel Latham in the eighth.