Theo Pinson scored 11 and Brice Johnson had 10 points for the Tar Heels (5-1), who trailed 67-59 with just more than 4 minutes remaining before their game-ending charge.
Kamau Stokes hit six 3-pointers and finished with 24 points for the Wildcats (4-1), but the freshman also committed a pair of costly turnovers in the closing minutes. Justin Edwards added 10 points.
Meeks started the Tar Heels' final push with a pair of free throws, and Johnson added a putback moments later -- one that perhaps could have been called interference. Joel Berry II added a 3 from in front of his own bench, and Jackson scored on a drive to the basket.
By the time Meeks stripped Stokes near midcourt and went in for an uncontested dunk, the Tar Heels had seized a 70-68 lead over the stunned Wildcats.
Pinson added a 3-pointer of his own moments later to put the game away.
The Tar Heels won the tournament without Marcus Paige, their All-America guard who is out with a broken hand. Coach Roy Williams said Monday night that Paige could have played if this was the NCAA Tournament, but he wanted to give his floor leader as much time as possible to heal.
North Carolina has beaten Kansas State four straight times, while Williams continued his mastery of the Wildcats. He was 35-4 against them as the coach of rival Kansas.
The first half Tuesday night was dominated by runs that ultimately led to a near-stalemate.
The Wildcats went on the first big charge, an 11-1 spurt capped by a jumper from Edwards that ignited a crowd full of purple-clad Kansas State fans. But the Tar Heels answered with a 13-2 run of their own, taking a 24-19 lead on Jackson's basket with 6 minutes left in the half.
Kansas State struggled from the field but had success getting to the rim, where the Tar Heels resorted to fouling. The Wildcats made enough free throws to forge a 32-30 lead at the break.
It remained nip-and-tuck most of the second half.
North Carolina pushed ahead 46-42 on a bucket by Isaiah Hicks, only for the Wildcats to come back and take a 53-48 lead when basket interference was called on Stephen Hurt's shot.
The Wildcats took their biggest lead of the game at 67-59 when Hurt hit a 3-pointer and then scored inside with 4:19 remaining.
North Carolina: Paige was once again in uniform but remained on the bench. ... Williams has more wins against Kansas State than any other opponent.
Kansas State: All four of the Wildcats' losses to North Carolina have come on neutral floors, including their last meeting in 1989 in Charlotte. ... Stokes had been 3 for 14 from beyond the arc in the Wildcats' first four games.
North Carolina takes on former ACC rival and second-ranked Maryland on Dec. 1.