After a thrilling upset win over then-No. 20 West Virginia in overtime Saturday, the Texas Longhorns let some air out of the NCAA Tournament bubble and are now close to securing a spot in the 68-team bracket.

All that’s left to do to seal that reservation is win a Big 12 tournament game.

“Last year, we weren’t even in the conversation, but this year we’re on the bubble,” junior guard Kerwin Roach II said. “Not making it would hurt, so we just gotta go out there and play every game like it’s our last. And once we do that, we’ll ball out and just hope for the best.”

Texas checks into the Big 12 tournament in Kansas City as the conference’s No. 7 seed, paired up against No. 10 seed Iowa State. The favored Longhorns have already downed the Cyclones twice this year, but no team is better at making surprise runs in the conference tournament than the squad from Ames.

Iowa State is the defending Big 12 champion and has emerged victorious from three of the last four conference tournaments. Despite riding a six-game losing skid and finishing dead last in the league, the Cyclones recorded three ranked Big 12 wins, including an 18-point win over Texas Tech and a 16-point win over West Virginia.

After the shorthanded Longhorns stunned the Mountaineers on Saturday without injured freshman center Mo Bamba (toe sprain), Texas’ odds of qualifying for its second tournament under head coach Shaka Smart spiked to 98 percent, per ESPN’s Basketball Power Index (BPI). Smart’s team now boasts a solid resume that includes 18 wins and five ranked victories despite a brutal conference schedule.

But the work is not done yet, as ESPN chief bracketologist Joe Lunardi has Texas slated in for a play-in game in Dayton, Ohio, prior to the opening Round of 64.

“We really want to get in the tournament,” Smart said after the West Virginia win. “You can’t build up this mindset in your head that if a certain game doesn’t go your way, you want to jump off the top of a building. You just don’t want guys thinking that way.”

With Bamba’s status still in question, the Longhorns must deliver a performance similar to Saturday’s 3-point shooting barrage to continue to win in Kansas City. Texas played just seven members of the roster against West Virginia. But shooting 56.9 percent from the floor and 57.9 percent from three springboarded the Longhorns to a near-NCAA Tournament-clinching win.

“This was the best with the most on the line,” Smart said of the team’s performance against West Virginia. “I told the guys the other day, the only chance we have to win is if winning can be bigger than any of your individual agendas. We have no chance to win if winning’s not bigger than them.”

To avoid a potential play-in game in Dayton and land a spot in the Round of 64, the Longhorns will have to rely on several emerging contributors, including freshman power forward Jericho Sims. The Minneapolis, Minnesota, native dunked all over the Mountaineers en route to a career-high 17 points and eight rebounds. After stepping up for Texas with the season on the line, Smart can already see Sims’ progress.

“Obviously with Mo being down the last two-and-a-half games, that adds to the urgency of what we need from (Sims),” Smart said. “He’s got unbelievable athleticism and a great upside. But the thing that he’s done lately is he’s actually played. He’s actually gone and made plays. I thought he was huge grabbing the ball for us and obviously finishing around the basket.”

Sims and the rest of the young Longhorns squad will take the court against the Cyclones at 8:30 p.m. Wednesday.