KANSAS CITY, Mo. — There are plenty of trophies in Bill Self’s office, but there is no time machine.

Still, if a visitor from the far-off future of, say, late Thursday evening would’ve come to the Kansas basketball coach ahead of his team’s clash with Texas in a Big 12 Tournament quarterfinal at Sprint Center and spoiled the big-picture details of the result, the Hall of Famer would’ve probably flashed a grin.

While the more minor aspects of the No. 17-ranked and No. 3-seeded Jayhawks’ 65-57 victory left Self vexed, the outcome didn’t — and neither did the golden opportunity now at his team’s fingertips.

“If you told us before the game started — what was it, an eight-point (margin of victory) — and we’d hold them to 57, I would’ve said, ‘That’s how you win games in March. You make other teams not play as well as they normally do,’ ” Self said. “So I’ll take this one and be happy with it, but I know we can be a lot better.”

Devon Dotson scored 17 points and helped the Jayhawks to a 17-0 advantage in points in transition, while the KU defense held Texas to a 35.7-percent shooting clip in the contest. The Longhorns cut the deficit to four with 2:43 remaining but came up empty on their final four possessions, with Quentin Grimes hitting 4 of 4 free-throw attempts along the way to ice the outcome for the at times offensively challenged Jayhawks.

The victory clinched an 8:30 p.m. Friday semifinal appearance for KU against No. 10-seeded West Virginia, which stunned No. 2 seed Texas Tech in a 79-74 outcome earlier in the evening. A victory against the last-place Mountaineers would send KU to a 5 p.m. Saturday tourney championship tilt against either top-seeded Kansas State or No. 5 seed Iowa State, who meet in a 6 p.m. Friday semifinal.

Contested in front of a partisan Jayhawk crowd, Thursday’s quarterfinal was, to put it candidly, a bit of a snooze-fest.

KU and Texas entered the intermission locked at 29, the result of a listless first half. The Jayhawks (24-8) scored 18 points in the paint thanks to nine points apiece by Dedric Lawson and David McCormack, and Dotson pitched in eight, but the team struggled to find offensive rhythm — Lawson’s trey with 4:10 left represented the first and only long-range make for KU ahead of the break. Texas, meanwhile, was hampered by foul trouble for standout freshman forward Jaxson Hayes, who played just four minutes before the break.

The Jayhawks — and as a result the Sprint Center crowd — finally came to life in the early goings of the second period.

Lawson’s mid-range jumper on the team’s first possession kick-started a stretch that saw KU hit 5 of 7 field goal attempts to open the final period, capped with a Dotson corner trey that gave the group a 42-35 advantage. McCormack made the lead nine with an offensive rebound and layup moments later, and a subsequent Grimes trey made KU 8 for 13 in the half and kept the Longhorns (16-16) at bay.

Grimes’ driving transition layup gave KU a 54-43 advantage with 9:53 remaining, but it represented the last offensive gasp for the Jayhawks for an extended stretch — KU endured a six-plus-minute field goal drought, a run Dotson ended with layup that put KU up 60-52 with 3:25 remaining, but even that represented the team’s final made shot.

Texas, though, struggled to take advantage. While a layup in traffic and made 3-pointer from Kerwin Roach — the senior guard was playing his first game since a Feb. 22 suspension for a violation of team rules — brought the Longhorns within four, 61-57, with 2:43 remaining, the No. 6 seed didn’t score again. Hayes went down with an apparent left knee injury at the 2-minute mark on the first possession of four straight empty ones for Shaka Smart’s squad, and Grimes hit all four of his free-throw tries at the same time to ice the outcome.

“It was definitely just a game of runs,” said Grimes, who finished with 12 points. “We got out and we made them play bad and we got in transition and made some easy buckets. ... They kind of knew most of the sets we were running and we knew the sets that they were running. Sometimes it comes down to players making plays and I felt like we did that.”

Lawson scored 16 points and grabbed six rebounds but went 6-for-15 from the field and committed six turnovers, the perfect representation of the uneven evening for KU.

“Six turnovers and playing out of double teams when he’s got guys wide-open? He’s got to do a better job of being able to close out possession for us,” Self said of Lawson. “But I thought our front line actually did well against theirs.”

The freshman forward McCormack scored 13 points on 6-for-7 shooting and grabbed nine rebounds to continue his recent torrid stretch.

“He’s slowed down a lot offensively so he’s not quite as sped up. I’m real pleased with him,” Self said of McCormack. “He’s really improved a lot and makes me think I wish I was playing him a lot more earlier in the season.”

Osetkowski’s 18 points paced the Longhorns.

Starting four first-year players in the postseason for the first time in his 16-year tenure, Self indicated most of the freshmen played beyond their years in their first one-and-done scenario.

“I thought David did. I thought Devon did. I thought Q (Grimes) did late. And I certainly think Ochai (Agbaji)’s got to get there, because he had a tough outing,” Self said. “But that’s a lot of young kids out there, and it’s a different type of pressure. But we did some good things.”

The Mountaineers (14-19) now await, but Self warned any onlookers already writing the Jayhawks into Saturday’s championship game to slow their respective rolls.

“Every team goes through ebbs and flows and ups and downs, but the team I watched play tonight is hungry,” Self said of WVU. “They’re playing with a free mind. The basket looks big to them and certainly they’re rebounding the ball like (Bob) Huggins’ teams have historically done at West Virginia.

“Forget about the records — when Kansas and West Virginia play you usually get your money’s worth as a game, and I’m sure it will be that way (Friday) night as well.”

No. 17 KANSAS 65, TEXAS 57

TEXAS (16-16)

Osetkowski 6-13 3-4 18, Hayes 0-1 2-4 2, Ramey 3-9 0-0 6, Febres 4-9 0-0 11, Coleman 1-5 0-0 3, Hamm 0-4 0-0 0, Hepa 0-0 0-0 0, Sims 3-3 0-2 6, Mitrou-Long 1-5 1-2 3, Roach 2-7 3-4 8. Totals 20-56 9-16 57.

KANSAS (24-8)

McCormack 6-7 1-3 13, D.Lawson 6-15 3-4 16, Dotson 6-11 4-5 17, Agbaji 1-5 0-1 2, Grimes 2-10 7-8 12, Lightfoot 0-2 0-0 0, Garrett 2-4 1-1 5, Moore 0-1 0-0 0, K.Lawson 0-0 0-0 0. Totals 23-55 16-22 65.

Halftime — 29-29. 3-Point Goals — Texas 8-25 (Osetkowski 3-7, Febres 3-8, Roach 1-3, Coleman 1-3, Mitrou-Long 0-1, Ramey 0-3), Kansas 3-11 (Dotson 1-1, D.Lawson 1-2, Grimes 1-6, Garrett 0-1, Agbaji 0-1). Fouled Out — None. Rebounds — Texas 31 (Osetkowski 7), Kansas 39 (McCormack 9). Assists_Texas 10 (Mitrou-Long, Ramey 3), Kansas 11 (Dotson 4). Total Fouls — Texas 19, Kansas 11. A — 18,927 (18,972).