Last Sunday, Knicks president Steve Mills and GM Scott Perry sat and watched the first quarter of the Knicks-Clippers matinee at the Garden, then headed for the exits.

The Knicks’ two top decision-makers took a flight to Tulsa, Okla., for the NCAA Tournament second-round matchup that night between Texas Tech and Buffalo.

“They wanted one more look,’’ an NBA source said.

They wanted one more look at 6-foot-6 sophomore shooting guard Jarrett Culver, who is heading to the NCAA Final Four in Texas Tech’s first-ever appearance.

“He’s going to be one of the best two-way prospects in the draft,’’ an NBA scout said.

Texas Tech is known for its suffocating defense and Culver, a versatile defender, is a big part of that. He’s also become a big scoring threat and is having a terrific NCAA Tournament, averaging 21.4 points in the four wins.

“Unbelievable,” Culver said after Saturday’s Gonzaga victory. “We’re not supposed to be here, man. It’s unbelievable.”

The key to the Knicks’ attraction to Culver is his defense. Knicks coach David Fizdale made a point last week to say the offseason goal is to add more defensive-minded players. It seemed an acknowledgment that the Knicks went for the shiny penny in last year’s lottery in selecting scoring forward Kevin Knox, whose defense is a major question mark.

The Knicks’ chance of winning the Zion Williamson lottery is now locked in at 14 percent. If they remain with the NBA’s worst record, they will have a 60 percent chance of falling to No. 4 or 5, where Culver, the Big 12 Player of the Year, should be available.

Culver, 20, was not a one-and-done guy. He ranked as the 312th-rated prospect in the 2017 recruiting class, according to 247Sports, and stayed home in Lubbock, Texas, to play in college.

“I’ve watched him play lots of games this year, and he has a quick first step,” Gonzaga’s Brandon Clarke said. “He can shoot it pretty well and obviously he’s pretty bouncy, too.’’

He was always considered a stout defender, but he rose up the mock drafts in late January because he’s become a scoring dynamo. He’s found anywhere from No. 3 to 11 in the most prominent mock drafts.

“I started way back in the summer, just working on technique and just to be a better shooter,” Culver said at the Sweet 16. “[There are] always ways you can improve on your game, and that was one of the ways I improved.”

The NBA scout added Culver is “strong mentally’’ and should be able to fix his weaknesses.

Fizdale’s Knicks have been abysmal this season and that’s why Culver could be a nice consolation prize if they fall back.

“Our defense won’t really get to where it’s at until we start to really fill in the gaps with the type of guys we think can take our defense to the next level,’’ Fizdale said. “Add maybe another forward defender or another perimeter defender that has a reputation for that. Those kind of guys are the ones that elevate your system to the next level. We’ve already started on the idea of the type of players we want and type of defense we want to play.”

The Knicks, who finish their six-game homestand vs. the Bulls Monday at 14-62, need to win four of their last six games to avoid making the record books for futility. If they go 3-3, the Knicks would share the worst record in franchise history at 17-65 with the 2014-15 edition. Anything worse and the 2018-19 Knicks will stand alone.