Butler, who has six game-winning baskets already this season, played his best during the first 20 minutes for the second-seeded Mountaineers on Sunday.
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That's when he scored 19 of his 28 points in leading the Big East Conference champions to a 68-59 victory over the 10th-seeded Tigers in the second round of the NCAA tournament.
"He's the 'Magic Man,'" Mountaineers point guard Darryl Bryant said of Butler. "He shows up when we need him. That's really the only thing that counts."
Butler accounted for nearly two-thirds of the Mountaineers 30 points in the first half, and played a key role in breaking down Missouri's high-pressure defense, which was dubbed "The Fastest 40 Minutes of Basketball."
"We didn't really panic," Butler said. "We just stepped up to the challenge and played like men and broke the press."
West Virginia (29-6) advanced to face No. 11 seed Washington in the East Regional semifinals at Syracuse on Thursday. It marks the fifth time the Mountaineers reached the final 16, and first since 2008.
Michael Dixon scored 15 points for Missouri (23-11), which was undone by an overall poor shooting performance. The Tigers went 20 of 61 from the field and were just as bad from the free-throw line, where they went 12 of 20.
"It's tough to win when you have guys shooting 2 for 9, 3 for 8," said Tigers forward Keith Ramsey, who went 2 for 9 for eight points. "It's tough and it's frustrating. If those shots had fallen, you'd probably be talking about us winning."
Missouri was denied a chance to return to the round of 16 in consecutive seasons, after they reached the final 8 last year.
Kevin Jones had 13 points and nine rebounds and Devin Ebanks added 14 points and seven rebounds for the Mountaineers. With the win, West Virginia matched a school record for victories set in 1958-59, the season the Mountaineers, led by Jerry West, went 29-5 and lost in the NCAA championship game.
Butler was the key, especially in the early going when the Mountaineers scored the first eight points and never trailed. He opened by hitting four of his first seven 3-point attempts and then closed the half by hitting seven of eight free throws.
Even the Tigers were left impressed by Butler.
"He stepped up to the plate and put his stamp on the game," senior guard J.T. Tiller said.
Down 50-41 midway through the second half, Missouri clawed back to get within three points with 4:36 left when Zaire Taylor hit a 3-pointer. That was as close as they would come.
Butler hit two free throws at the other end. Then, after Missouri's Kim English missed a 3-point attempt and Ramsey couldn't control the rebound, Ebanks hit one of two free throws to put West Virginia up 59-53. Missouri then went 3 minutes without a field goal.
"I thought it was a heck of a game," Tigers coach Mike Anderson said. "We got 3 minutes to go and we've got the ball. It's a four-point game. So it's a game that could've went either way."
It was a rough and tumble game between two aggressive defenses. Missouri entered the game leading the nation in forced turnovers and steals, but couldn't rattle the Mountaineers.
West Virginia was efficient in handling the ball and committed only 10 turnovers.
West Virginia capably neutered the Tigers pressure by getting the ball quickly up the court. And once they got into the offensive zone, the Mountaineers slowed the pace by working their half-court game to near perfection by running down the shot clock and attacking the basket.
"We wanted to be in an attack mode," Mountaineers coach Bob Huggins said. "And when you are as aggressive as they are, you're going to foul some."
The Mountaineers won despite going a stretch of 12:47 -- spanning halftime -- between field goals. The difference was getting to the free throw line. They hit 11 of 14 attempts and actually extended their lead during the stretch between Ebanks hitting a jumper in the paint to put West Virginia up 23-17 with 9 minutes left in the first half to Bryant hitting a transition layup that made it 36-29 with 16:13 left in the game.