KANSAS CITY, Mo. -- Rick Barnes has believed all along that Texas is safely in the NCAA tournament. That didn't stop him from playing a psychological trick on his team during an impassioned halftime speech Thursday night.

The Longhorns were struggling against Iowa State (No. 25 AP), and Barnes told them deep inside the Sprint Center to make their choice: the NIT or the NCAA tournament. They could make their decision over the final 20 minutes, effectively taking it out of the hands of a committee holed up in a board room.

"Let's just say we are on the bubble," Barnes recalled saying. "Now if I write down NIT or NCAA, which one would you put your name under? Which one? Whichever one you want, you have to earn it."

They certainly did.

Texas rallied from a big second-half deficit before J'Covan Brown converted a go-ahead three-point play with 36.3 seconds left, lifting the Longhorns to a 71-65 victory in the Big 12 tournament quarterfinals.

Texas will face fifth-ranked Missouri on Friday night for a spot in the championship.

Brown finished with 23 points for the Longhorns (20-12), who reached the 20-win plateau for the 13th consecutive season and just maybe ensured another streak would remain intact: The school has gone to 13 straight NCAA tournaments, tied for fourth-most behind Kansas, Duke and Michigan State.

"Tournament time is always a great time," Brown said. "The crowd, I think we only had a couple fans, and they had a great amount of fans. We love that, to walk into a gym and quiet their fans. We just tried to give it our all for 40 minutes."

Royce White had 17 points and 10 rebounds for the Cyclones (22-10), and it was his turnaround bank shot with 51.6 seconds left that tied it 65. But after Brown was fouled on a spinning jumper and made the free throw, White lost control of the ball with 22.9 seconds left.

It wound up in the hands of the Longhorns' Jonathan Holmes, who made both free throws for a 70-65 lead. The Cyclones turned it over again on their next possession to seal the outcome.

"It means nothing. My performance was not good enough," said White, who was voted the league's top newcomer. "It just wasn't good enough."

Myck Kabongo added 11 points and Clint Chapman had 10 for Texas, which trailed by 11 early in the second half before embarking on a 22-4 run to flip the script. Then it came down to which team could make the clutch plays, and Brown was able to deliver for Texas.

The Cyclones, who most believe are squarely in the dance, haven't won a Big 12 tournament game since 2005. They've dropped seven straight, four of them at the Sprint Center.

"It's disappointing to go out in the first round down here, especially all the fans we had in attendance," Cyclones coach Fred Hoiberg said. "They made big plays. I thought we put our heads down as a team, and then we regrouped and found a way to get back in the game.

"They made plays down the stretch and we didn't."

Indeed, it seemed like the old days for Iowa State for a while.

Fans carried Hilton Magic down Interstate 35 during the early years of the Big 12 tournament, turning the old Kemper Arena into a homecourt advantage. Sprint Center felt a bit like that against Texas, with red- and yellow-clad fans filling the place for the day session and then filing right back in at night.

They announced their presence as Iowa State seized a 28-19 lead late in the first half behind balanced scoring up and down the lineup, and really grew to a roar when the lead swelled to 40-29 on Scott Christopherson's jumper by with 17:10 remaining in the game.

"I did get upset because we started the half by taking a quick shot, and then we threw it out of bounds. It was our offense," Barnes said. "All year we've guarded."

Well, the offense finally started clicking.

Kabongo and Julien Lewis combined for an 11-0 run that was part of a larger 22-4 stretch in which that 11-point deficit turned into a 51-44 lead. Brown knocked down a couple of shots, but mostly he played the distributor to teammates who at times have gone missing this season.

Texas still led 55-47 when the Cyclones clawed back, tying it at 59 on a pair of foul shots by Chris Allen with 4:39 left. The Longhorns answered with six straight points, four of them on jumpers by Brown, and maintained a comfy cushion with 2:35 left in the game.

Iowa State rallied one more time, getting a basket from Allen and another from Percy Gibson to pull within 65-63. White managed to get the Cyclones even, but Brown was there to answer for the Longhorns, and Texas took control in the closing seconds.

"We've got one more chance to go out and make a run and do something," Hoiberg said, "and hopefully we'll be better next time."