On the other hand, Texas sits at home hoping they've done enough at 30-22 to make the NCAA Tournament.
"We're disappointed, we knew the meaning of this going into it," said Texas head coach Augie Garrido. "We don't know what the committee is [going to do], how they're going to respond, and we don't know what this means to us. But we'd have rather won the two games that we lost and we'd feel a whole heck of a lot more secure about being in the playoffs had we won this game."
Kansas, the conference's No. 7 seed entering the tournament, took an early 3-0 lead after the first inning courtesy of some successful small ball.
Two bunts and a throwing error by Texas third baseman Erich Weiss allowed the first run to cross.
An RBI groundout set the stage for first baseman Chris Manship's RBI double into the right center gap giving the Jayhawks a three-run advantage.
"Today's game was decided by the first inning when they scored three runs on two bunts," Garrido said. "That's why we like to bunt, and that's what it does to the defense. They got a timely hit to end up with three in that inning."
Meanwhile, Texas couldn't capitalize at several key times.
They stranded eight in the contest and left runners at third in the second, fourth, fifth, sixth and ninth innings.
Texas did make it a 3-1 game on Weiss' RBI single up the middle in the top of the third.
But Kansas added another in the fifth when catcher James Stanfield singled home second baseman Ka'iana Eldredge.
It stayed 4-1 until the ninth when things got very interesting.
The Longhorns put runners on second and third by virtue of a walk, single and wild pitch.
Texas designated hitter Kevin Lusson then ripped one to first that Manship couldn't handle, scoring one run.
Manship also errantly threw it down the line in front of the plate on the plate, but the runner rounding third held, and Lusson was caught trying to advance to second.
Texas right fielder Mark Payton, who finished 1-for-4 with a run scored, then struck out to end the contest.
"We didn't play that great," Payton said. "We played pretty good, but Kansas played a great game on the other side of the field. We didn't get the big hit, and that's kind of what happened."
A lot of that credit goes to Jayhawk starter Wes Benjamin, who logged six innings of one-run ball, striking out a pair and surrendering just five hits en route to picking up the victory.
"I was working pretty well today," Benjamin said. "I noticed in the bullpen I wasn't as sharp as I would normally like to be. We got out of a couple of key situations we needed to get out of."
Stanfield led the way for Kansas, going 2-for-4 with an RBI and run scored, while Manship also had a pair of hits and RBI.
No one had more than one hit for the Longhorns, as Weiss and Lusson recorded the only RBIs.