The Cyclones (28-7) head to Madison Square Garden next week to face No. 7 seed Connecticut in the East Regional semifinals.
The Tar Heels (24-10) are gone in the NCAA tournament's opening weekend for the first time in consecutive seasons under coach Roy Williams.
North Carolina's Nate Britt raced the ball up court after Kane's basket, but time expired before he could reach midcourt and call a timeout. Officials huddled for several minutes reviewing clock replays before ruling the game was over.
Right away Williams - who collapsed his hands on his knees as Britt dribbled toward him and the buzzer sounded - shook Iowa State coach Fred Hoiberg's hand as North Carolina began absorbing a last-second heartbreaker.
Kane finished with 24 points and 10 rebounds. It was just the kind of big game the Cyclones needed without forward Georges Niang, who broke his foot in Friday's win against North Carolina Central. The 6-foot-7 sophomore sat on the bench wearing a bulky boot while the Cyclones tried their best without their third-leading scorer and tallest starter.
Marcus Paige led North Carolina with 19 points and Kennedy Meeks had 15 points and 13 rebounds. But North Carolina played nearly the entire game without forward Brice Johnson, who sprained ankle in the opening minutes.
The team said X-rays were negative, but the Tar Heels' third-leading scorer never returned.
Big 12 player of the year Melvin Ejam had 19 points for the Cyclones and Monte Morris added 13.
The Tar Heels crave a fast pace, and - after dealing with the grind-it-out style of recent opponents - Williams and Paige had spoken of relishing the chance to finally hit the gas against the similarly up-tempo Cyclones.
But this was no track meet.
Undersized Iowa State bottled up the Tar Heels before they could run and bombarded them with 3-pointers (12 of 26) instead of quick baskets. The first dunk came from Kane, not the high-flying Tar Heels, and not until 12 minutes into the game after a handful of bungled North Carolina fast breaks.
Niang's injury left Hoiberg with a tough choice: go small with his best remaining five or a put a little-used big man in place of his star sophomore. He opted for size over another shooter, giving 6-foot-8 forward Daniel Edozie his first career start.
Edozie missed the only two shots he tried and grabbed four rebounds. But Johnson's bum ankle cut North Carolina down a size on its own.
Johnson, who came in averaging 10.6 points and is the Tar Heels' second-leading rebounder, tumbled to the floor with North Carolina up 12-7. He sat on the bench before hobbling to the locker room, and while the team said X-rays were negative, it announced just before the second half that he wouldn't return.
Coincidental or not, the Cyclones got hot the moment Johnson left the game.
They shook off a 1-for-10 start from the floor and erased a seven-point deficit in less than 1 ½ minutes. After that, neither team led by more than single digits.