A clear lane to the basket, a quick drive into space and a tough shot that went in while he was fouled with 5.5 seconds left.
Taylor made the free throw, DeMarre Taylor added one more 2 seconds later after a Texas turnover and the Tigers were skipping off the court with a 69-65 upset victory, their first on the 16th-ranked Longhorns' court since 1999.
The last time the Tigers won in Austin was former longtime Missouri coach Norm Stewart's last career victory before he retired.
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"We wanted to spread the floor. I saw the lane. I knew time was going down and I had to make the play," Taylor said. "I figured it was the best shot we could get at the time."
It was good enough to send the frustrated Longhorns to their second straight home loss just a few days after Kansas State snapped their 19-game home winning streak.
Texas had tied it at 65-65 on A.J. Abrams' floater in the lane with 1 minute to play. But Abrams, the Big 12's career leader in 3-pointers, missed from long range with 28 seconds left, giving Missouri a chance to set up for the winning shot.
After Taylor's play, Carroll intercepted the inbounds pass, drew a foul and hit one of two free throws to seal the win. Taylor finished with 17 points for the Tigers (19-4, 6-2).
Dexter Pittman scored a career-high 25 points for the Longhorns (15-6, 4-3).
Pittman and his 6-foot-10, 300-pound body had a huge game for the Longhorns. His large frame and hands dominated the Tigers under the basket with 9-of-12 shooting. He played a career-high 23 minutes.
"Dexter was a beast out there and all my scrawny little guys were falling everywhere," Missouri coach Mike Anderson said.
But Pittman's foul troubles in the second half kept Texas from finding any kind of offensive rhythm and turned him into a defensive liability in the final minutes.
The teams were tied or traded the lead eight times in the final 5 minutes. Pittman's dunk with 3:01 to play gave Texas its final lead at 62-60 before Leo Lyons answered with two straight baskets -- both coming when he drove right by a passive Pittman -- for the Tigers.
Lyons finished with 14 points and Carroll had 13 for the Tigers. Abrams scored 11 for the Longhorns but continued to struggle to find his long-range stroke at critical times.
The Longhorns also missed their usual production from Damion James, who came in with eight double-doubles this season but finished with just six points while battling a sore knee.
"We've got to be smarter, and we've got to stop playing streetball," Abrams said. "Everybody's got to look at themselves and do better."
Pittman's 11 minutes in the first half nearly equaled his season average and he scored 14 points on 5-of-7 shooting. On one possession he twice went up over three Tigers for a rebound before a powerful dunk. Texas built a 26-16 lead before the Tigers rallied to cut it to 34-29 at halftime.
Texas struggled to score in the second half as the Tigers applied full-court pressure. The Longhorns managed just three field goals in the first 8 minutes of the half and Missouri took a 46-42 lead on consecutive layups by Carroll, the second coming when he blew past Connor Atchley in the lane. Missouri forced 15 turnovers, turning them into 14 points.
"We call it organized chaos," Carroll said. "You don't know what we're going to do, when we're going to do it, when we're going to trap."
Pittman returned with 10 minutes to play and another rim-shaking jam got Texas within 50-49.
But even when the Longhorns could grab the lead, the Tigers wouldn't let them hold it.
After a dunk by James put Texas up 53-52 and brought the home crowd to its feet, Missouri got 3-pointers from Taylor and Matt Lawrence to settle them down again.
"We've just got to figure out our team identity," Pittman said. "Everybody's got to find their role and when they figure out their role they've got to come with their `A' game every night."