Baylor advanced after 10 innings against Oregon State.
OMAHA, Neb. -- Texas set a record with its 75th College World Series win Monday night, riding the strong pitching of Kyle McCullough to a 5-0 victory over top-seeded Tulane.
In its fourth straight and record 32nd appearance overall at the CWS, Texas passed Southern California's mark of 74 victories.
The Longhorns, unbeaten in two games so far this year, advance to a Wednesday night game at Rosenblatt Stadium against the winner of tonight's Tulane-Baylor elimination game.
Texas (53-16) scored two in the first off Tulane's top lefty, Brian Bogusevic, added two more in the fifth and another in the sixth, while collecting 12 hits.
The Longhorns got a stellar catch from right fielder Nick Peoples when he jumped against the right field wall in the eighth to take an extra base hit away from Micah Owings.
McCullough (11-4) pitched out of a first-inning jam and allowed six hits in seven shutout innings with three walks and seven strikeouts. J. Brent Cox pitched the final two innings to complete just the sixth CWS shutout since 1994.
It was also Texas' first shutout at the CWS since 1983 when Calvin Schiraldi blanked James Madison.
The Longhorns wasted little time in jumping on Bogusevic (13-3), with a first-inning error by shortstop Tommy Manzella leading the way.
Manzella picked up leadoff hitter Peoples' bouncer and threw over first. Peoples moved up on a sacrifice and then used a nice slide at the plate to just beat center fielder Nathan Southard's strong throw after a bloop single by Seth Johnston.
Will Crouch and Carson Kainer singled to load the bases, and Taylor Teagarden delivered the Longhorns' fourth straight hit to score Johnston.
McCullough gave up a pair of two-out hits in the first, a single by Manzella and a double to Owings before retiring Mark Hamilton on a fly ball.
Texas made it 4-0 in the fifth on David Maroul's two-out, two-run double past third.
The speedy Peoples beat out an infield hit to short in the sixth, moved up on another sacrifice and came home on Crouch's RBI single off the left field fence.
Bogusevic, a first-round pick of the Houston Astros, gave up 11 hits and five runs in seven innings as Tulane fell to 55-11.
Johnston's first-inning was his 112th hit of the season.
Baylor 4, Oregon State 3,10 innings
OMAHA, Neb. -- Baylor extended its first College World Series appearance in 27 years by at least one day with its first win in the tournament.
Mike Pankratz, batting .193, blooped an RBI single over first baseman Andy Jenkins and just out of the reach of second baseman Chris Kunda, ending the Beavers' first appearance in the CWS since 1952.
Jeff Mandel (4-0) got the win for Baylor (45-23) after holding Oregon State (46-12) to one hit in 42/3 innings of relief.
Josh Ford reached base safely leading off the 10th against Kevin Gunderson (6-4) after Beavers shortstop Darwin Barney couldn't field a high-bouncing grounder. Ford advanced to second on a sacrifice before Reid Brees singled through the left side of the infield to put runners on first and third.
Pankratz, who entered the game as a pinch hitter in the eighth inning, then got the game-winning hit on an 0-1 pitch.
Gunderson was effective in his 41/3 innings of work, holding the Bears hitless until Ford's single in the 10th.
Baylor starter Trey Taylor couldn't make it out of the second inning after walking five of the 10 batters he faced.