Isaiah Hicks came up big late, too, with a dunk and four free throws in the final 2 minutes to help UNC survive.
Daryl Macon scored 19 points to lead the eighth-seeded Razorbacks (26-10), who did everything right in the second half — except close out the Tar Heels.
The Razorbacks had UNC wobbling with their aggressive, mistake-forcing defense harassing the Tar Heels all over the court. And when Jaylen Barford scored in transition off a turnover, Arkansas led 65-60 with 3:28 left.
But the Tar Heels — loaded with returnees from a team that played in last year's national championship game — responded in a huge way.
Joel Berry II hit two free throws with 2:56 left, Jackson found Hicks for a dunk, then Hicks hit two free throws after being fouled on a rebound to put UNC up 66-65 with 1:44 left.
Then came Meeks' big moment. With the shot clock winding down, Berry drove and collided with Adrio Bailey, forcing him to just fling the ball onto the backboard to avoid the travel. Meeks, battling for position with Moses Kingsley inside, tapped it up and in to push the Tar Heels to the 68-65 lead.
Arkansas also squandered its chances to reclaim momentum, namely with Kinglsey missing two free throws with 25.2 seconds left while Anton Beard followed with a missed 3-pointer for the tie.
Hicks hit two more free throws with 10 seconds left to make it a two-possession game and all but seal it.
Arkansas: Coach Mike Anderson said the Razorbacks wouldn't change what they do against the go-go-go Tar Heels. His team rallied from 30-13 down to take its first lead midway through the second half behind a "40 Minutes of Hell" familiar edge from the Nolan Richardson era. In the end, though, Arkansas fell to 0-9 against No. 1 seeds in the NCAAs and couldn't reach the Sweet 16 for the first time since 1996.
UNC: The Tar Heels talked all season of returning to the Final Four after last year's title-game loss to Villanova. They said experience from that run would help them — and it did with their season in peril.
North Carolina advanced to the Sweet 16 to play fourth-seeded Butler on Friday in Memphis, Tennessee.