Zeke Mayo had 21 points and KJ Adams Jr had 14 for the Jayhawks (2-0), who led 49-29 in the first half but trailed 87-83 with 3:28 to go. Dickinson and Mayo responded with a series of baskets to tie the game at 89, and Dickinson's basket with 1:15 to go and free throw with 12 seconds remaining made it a three-point game.
The Tar Heels (1-1) raced up the floor, but Cadeau's 3 from the wing was contested and never had a chance.
"Total class on both sides. It was cheer your team but don't get after the other team," said Kansas coach Bill Self, who matched building namesake Phog Allen for the most wins at the school with his 590th. "Even though we didn't play our best, we found a way to win. I think it was a good game for both programs."
Seth Trimble scored 19 points to lead North Carolina. RJ Davis had 16 points and Cadeau finished with 12.
It was just the 13th matchup of the Tar Heels and Jayhawks, and the first since Kansas rallied from a 16-point deficit to win the 2022 national championship. The only other time they met on campus was in 1960 when Larry Brown - who would later coach the Jayhawks to the 1988 title - helped the Tar Heels win in Allen Fieldhouse.
Kansas made a repeat seem unlikely when it built a 20-point first-half lead and had the Tar Heels looking outsized and overmatched.
But the Tar Heels trimmed the deficit in the second half, and Jae'Lyn Withers' 3-pointer gave them an 80-79 lead with 7:06 to go. The teams wrestled it away several other times before Kansas finally put the game away.
"I mean, any time you bring two unbelievable programs that have terrific kids and talented kids - competitive kids - it doesn't matter whether it's March or November. It's going to be competitive," North Carolina coach Hubert Davis said.
North Carolina stayed alive by getting to the basket and drawing fouls, ultimately going 28 of 31 from the line. But the lack of production in the paint was a big problem.
For Kansas, the Jayhawks avoided what would have been the biggest blown-lead loss in school history.
Dickinson's basket inside with 1:15 left gave Kansas the lead, and the All-American center's free throw forced North Carolina into needing a 3-pointer to tie the game.
"You run through that tunnel and you see that crowd, and you see Kansas across the court," Davis added. "If you can't be fired up to play and compete in this type of atmosphere, against that type of team, something must be wrong with you."
North Carolina returns to action next Friday night against American. The Jayhawks play Michigan State on Tuesday night in Atlanta.
The Associated Press contributed