Thomas Robinson had 18 points and 15 rebounds against the 11th-seeded Wolfpack (24-13), Jeff Withey blocked 10 shots to finish one shy of the NCAA tournament record.
But Kansas shot less than 38 percent from the field, and made only one — count it, one — bucket from 3-point range.
"There's nothing we're doing wrong," Robinson said. "The looks are there. The shots are just not going down. So just keep running our offense, keep doing what we do and we won't do anything different. Like I said, (the lid) will come off eventually."
C.J. Leslie had 18 points to lead N.C. State, despite sitting much of the second half with four fouls. Scott Wood finished with 12 points on 2-for-10 shooting, though his biggest error wasn't a missed shot but the shot he never even got to attempt.
N.C. State had pulled within 58-57 on a transition layup by C.J. Williams with just over a minute remaining. The teams swapped possessions before Kansas managed to get a layup from Elijah Johnson off an inbound pass from Taylor with 13.5 seconds left.
The Wolfpack crossed midcourt and called a timeout to set up a play, which was designed to get the ball to Wood off a baseline pass. Instead, a skip pass went high and the sharpshooter stepped out of bounds trying to pull it in, giving the ball back to Kansas with 5 seconds to go.
Robinson was fouled and missed the free throw at the other end, but a pass down court and Howell's tightly guarded shot at the buzzer came up nowhere close, allowing Kansas to escape.
"We've got to play better," Self said. "But we're so fortunate and happy we get an opportunity to try and do so."
- Ranking the best running backs in BYU history
- Chris McGown resigns as BYU men's volleyball...
- Doug Robinson: Witt latest BYU runner chasing...
- Morning links: BYU's football schedule...
- Gallery of champions: All 94 state...
- Former Ute player among those invited to work...
- Rock On: BYU finds another recruiting niche
- Morning links: NBA post-up is not dead;...
- Report: Former Jordan High quarterback... 47
- Dick Harmon: NCAA's move to speed up... 46
- Morning links: BYU's football schedule... 43
- Rock On: BYU finds another recruiting... 39
- BYU football signs New Zealand rugby... 24
- Chris McGown resigns as BYU men's... 12
- Doug Robinson: Witt latest BYU runner... 8
- Utah State basketball: Aggie men to... 6