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KANSAS CITY, Mo. -- The beauty of Kansas basketball is the wealth of options in times of need.

On Saturday, it was the turn of Devonte' Graham, the tournament's outstanding.

Graham led the top-ranked Jayhawks with 27 points as they claimed the program's 10th tournament crown with a 81-71 victory over No. 9 West Virginia in the title game of the 20th Big 12 Championship at the Sprint Center.

Graham was 5-of-6 from 3-point range, and he and fellow point guard Frank Mason keyed an attack that didn't fold under the intense pressure from West Virginia.

"Frank and Devonte' did a great job, and I thought Wayne did a good job inbounding the ball," Kansas coach Bill Self said. "I think if you (had) told me we'd have 14, I'd probably (have) been, 'OK, we'll take that.'

"We had more than that, but a lot of them were us. I thought early we handled the press good, but then when we got numbers, we screwed up numbers."

The Jayhawks (30-4) shot 60 percent (9-of-15) from 3-point range, compared to 13 percent (2-of-15) for West Virginia.

"Kansas is the best team in the country," West Virginia coach Bob Huggins said. "We lose by 10. They shoot 60 percent from 3-(point range), we shoot 13 percent. And we turned it over 20 times.

"We're not going to win (like that); that's just an impossibility. We've got to get a lot more shots than what our opponents do. We only got nine more shots, but that's because we threw it to them. We're a very charitable bunch."

West Virginia (26-8) was led by forward Devin Williams with 31 points. He was 9-of-12 from the field and 13-of-15 from the line. He was the only West Virginia player in double figures.

"I just focused in," Williams said. "I just wanted it so bad for my guys and for this program. I was just trying to do whatever it took to get, you know, get the win."

Huggins was more complimentary.

"That's the best he's finished all year," Huggins said. "Devin is a really good player. I mean, he works extremely hard, he puts in extra time. He's the guy that we go to when things aren't going the way we would like for them to go."

Besides Graham's 27 points, guard Wayne Selden added 21 points and forward Perry Ellis had 17 for Kansas.

"We've got a special group of guys that can shoot the ball, and we have two point guards that can get in the lane," Selden said. "We have bigs that can pass the ball.

"There were a lot of traps, so we found ourselves open shots. Nobody really shies away from the big shot on this team. Anybody can knock it down, and tonight we showed it."

The Jayhawks followed an often-repeated theme this year of sputtering early and then turning it on in the second half. They outscored the Mountaineers 48-37 in the second half.

Kansas started much more quickly in the second half than they did in the first, scoring the first seven points to take a 40-34 lead. When Graham hit his third 3-pointer of the half, the Kansas lead was 51-39 with under 15 minutes left.

West Virginia rode Williams' shoulders to cut the lead to 67-63 with 4:09 left. But Landon Lucas converted a traditional three-point play to stretch the lead to 70-63.

After Daxter Miles scored inside, Selden hit a 3-point shot at the shot-clock buzzer to give Kansas a 73-65 lead with 2:41 left.

Kansas hit six straight free throws down the stretch to seal the victory.

The Jayhawks head into the NCAA tournament as the likely No. 1 overall seed, and Self thinks his team is ready for the challenge.

"We've been on kind of a high here with momentum in the last six weeks or so," he said. "It's something that we certainly didn't want to lose or fight to have to get back. So I think our guys should be confident going into (next) weekend."

Kansas struggled early with three missed shots from the field and two turnovers on the first five possessions while falling behind 6-0.

The Jayhawks got untracked with the long ball, hitting 3-of-5 from 3-point range to take their first lead at 11-10.

Kansas gradually pulled away, leading by as many as eight points. But Williams and the Mountaineers wouldn't go away. Williams, who had 18 points in the first half, keyed a 7-0 run that tied the score 24-24.

The teams traded buckets the rest of the half and West Virginia went into the locker room with a 34-33 lead.

Kansas was led in the first half by Graham with 10 points.

NOTES: Kansas holds a 6-3 edge all-time against West Virginia, with all the games coming in the last four years since the Mountaineers joined the Big 12. This was the first meeting in the Big 12 Tournament final. ... Kansas was the top seed for the 13th time in the 20-year history of the event, including the last eight. ... The all-tournament team comprised Graham, Ellis, Williams, Buddy Hield of Oklahoma and Georges Niang of Iowa State.