KANSAS CITY, Mo. >> Kansas coach Bill Self predicted this week that a No. 1 seed would someday lose to a No. 16.

He didn’t know his Jayhawks would be trying to fend off being the first.

The South Region’s top seed needed 17 points from Jeff Withey, and a series of foul shots from Ben McLemore and Naadir Tharpe down the stretch, to hold off scrappy Western Kentucky 64-57 Friday night and avoid another upset on a day full of them in the NCAA tournament.

“We’re pleased we won, and didn’t play our best by any stretch,” Self said. “They controlled the game for the most part. We’re happy to advance, but certainly not pleased with how we played.”

The Jayhawks (30-5), flummoxed by the Hilltoppers’ full-court pressure, trailed 31-30 at halftime. Kansas eventually built an 11-point lead in the second half, but couldn’t put Western Kentucky away until McLemore’s two foul shots with 11 seconds left.

McLemore and Travis Releford scored 11 each for the Jayhawks, who wearily advanced to play No. 8 seed North Carolina and former coach Roy Williams in the South Regional on Sunday.

“A North Carolina-Kansas game, everybody comes to play,” the Jayhawks’ Elijah Johnson said. “Roy is coming back, there’s going to be a lot of fans pumped up, and we’ll be pumped.”

The marquee matchup between a pair of college basketball blue blood almost didn’t happen.

North Carolina squandered a big lead before holding on to beat Villanova 78-71, and then the Jayhawks watched Western Kentucky do everything it could to spring one more upset.

Jamal Crook scored 13 points and T.J. Price had 12 for the Hilltoppers (20-16), who would have made history by becoming the first No. 16 seed to upend a No. 1 seed.

“We knew what we had to do,” Crook said, “regardless of what seed we were.”

Earlier in the day, No. 15 seed Florida Gulf Coast stunned second-seeded Georgetown, perhaps emboldening the Sun Belt champions. And on the same floor at the Sprint Center, 13th-seeded La Salle knocked off Kansas State and No. 12 seed Ole Miss beat fifth-seeded Wisconsin.

Alas, the undersized team in red couldn’t hang tough with the bigger guys in blue down the stretch, allowing Kansas to reach 30 wins for the fourth straight season — the first time that’s happened in Division I men’s basketball, after Memphis was forced to vacate the 2008 season.

“They kind of surprised us with how good they were, to be honest,” Withey said. “We definitely took them lightly, being a No. 1 seed. They came out and fought us really hard.”

Since the NCAA tournament expanded to 64 teams in 1985, 16 seeds are winless against No. 1 seeds in 116 games, including Southern’s heartbreaking 64-58 loss to Gonzaga on Thursday.

“I think the entire country got a glimpse of what they’re made of, a lot of character, a lot of heart,” Western Kentucky coach Ray Harper said. “A lot of people doubted us this season. We went through a lot of adversity, and adversity will tell you a lot about people.”

Western Kentucky spent the first half pinning Kansas against the ropes.

Price hit an opener 3-pointer in the opening minute, George Fant was able to use his superior quickness against the bigger Withey in the paint, and the Hilltoppers — who needed four wins to capture the Sun Belt tournament title and the league’s automatic bid — slowly built a 20-16 lead.

The heavily pro-Kansas crowd fell quiet, even as Jayhawks coach Bill Self turned up the volume on the sideline, laying into his team for its lethargic start.

Kansas finally pulled ahead for the first time since midway through the first half when Elijah Johnson finished off a three-point play that made it 28-27 with 90 seconds left, but a pair of baskets by Price down the stretch gave the scrappy Hilltoppers a 31-30 lead at the break.

The Jayhawks seized the lead again early in the second half when Kevin Young followed up his own miss by grabbing the rebound and throwing down a reverse jam, and then Releford scored off a nifty feed from McLemore, forcing Harper to burn a timeout.

Fant and Aleksejs Rostov both picked up their fourth fouls midway through the half, taking seats next to Harper on the Western Kentucky bench. But the longtime Division II and NAIA coach couldn’t keep his hottest hands there for long, and decided to gamble by putting them back in.

Harper rolled snake eyes when Fant fouled out with 5:37 remaining.

Withey made one of two free throws, McLemore drove untouched down the lane for an easy basket, and Withey scored on a nifty move in the post to push the Jayhawks to a 52-42 lead — their biggest of the game — and force Harper to call another timeout with 3:44 left on the clock.

Western Kentucky started whittling into the lead in the closing minutes, and a 3-pointer by Crook made it 59-55 with 25.4 seconds left on the clock.

But the Jayhawks got the ball in the hands of Naadir Tharpe, and he made two free throws to provide them a cushion. Price misfired from beyond the arc, and Brandon Harris was long on another 3-pointer from the corner, as McLemore added two more foul shots to seal the Jayhawks’ victory.

“Thankfully, we got the win,” Withey said, “and that’s all that matters.”