A 16-4 run over a 5½-minute second-half stretch was the key for Butler this time, turning a 43-41 lead into a 59-45 cushion.
Marcus Paige scored 18 for North Carolina (3-1), which allowed 29 offensive rebounds - matching the most by the Tar Heels under coach Roy Williams. Brice Johnson added 11 and Kennedy Meeks blocked five shots.
Butler shot 22 for 72 - and won anyway.
Paige was ice-cold early on a steamy day on the island, missing nine of his first 10 shots. But a pair of 3-pointers followed by a three-point play in a late 3- minute span pulled North Carolina within 69-66.
The Heels got no closer.
Barlow made two quick 3-pointers after halftime, putting North Carolina in a second-half hole for the first time this season.
The Tar Heels never emerged from it.
Whether it was from the field or the line, North Carolina just couldn't shoot. The Tar Heels missed nine of their first 14 free throws in the second half, going 1 for 13 from the floor during one stretch.
The Bulldogs, who came in with all eight of their regular rotation players shooting at least 50 percent this season, struggled to get anything to fall in the first half. But North Carolina let the Bulldogs hang around, a mistake that wound up being costly.
North Carolina: Meeks blocked three shots in the first 15:45, matching his career best for any full game. ... The Tar Heels had first-half scoring runs of 11-0, 12-0 and 11-0 in their first three games, but managed only one stretch of five unanswered points in the first half Wednesday.
Butler: The Bulldogs had lost their last seven games against Top 25 teams. ... Four of Butler's starters Wednesday played when the Bulldogs beat North Carolina in Hawaii two years ago. ... Starting guards had averaged 8.0 points against the Tar Heels in the season's first three games. Barlow had 11 by halftime.
North Carolina: UCLA in Thursday's consolation round.
Butler: Oklahoma in Thursday's semifinals.