After a one-year hiatus, North Carolina played like a team that wants an extended stay in the NCAA tournament — on offense, at least.
UNC (27-7) plays the winner of Friday's late game between Washington and Georgia on Sunday in a round-of-32 matchup.
Zeller, the 7-foot junior, scored 25 of his career-high 32 points in the second half as the Tar Heels rebounded nicely from last Sunday's 75-58 loss to Duke in the ACC tournament final.
Henson, the long-armed 6-10 sophomore and the ACC defensive player of the year, scored 20 of his career-high 28 points in the first half. He also had six of UNC's 10 blocked shots.
Barnes, the superb 6-8 freshman, added 24 points.
Long Island (27-7), the Northeast Conference champ, saw its 13-game win streak snapped because it was unable to match the Tar Heels' size.
The Blackbirds' tallest regulars, 6-7 Jamal Olasewere, 6-7 Julian Boyd and 6-7 Kenny Onyechi, were overmatched, though hardly intimidated.
Boyd finished with 18 points and Olasewere with 16. Sophomore guard C.J. Garner added 16 points.
Long Island's three-guard lineup tried to compensate with speed and 3-point shooting, but was unable to do sufficient damage from the perimeter. The Blackbirds were 8-for-31 from behind the arc.
Carolina was only 3-for-17 from 3-point range, with Barnes going 2-for-10. The Tar Heels outrebounded LIU 54-39 and made 31 of 42 free throws.
UNC led 53-42 at halftime. The Tar Heels stretched the lead to 21 points midway through the second half before an LIU run cut it to 77-67.
But Zeller scored seven consecutive points — part of a personal 11-point run — to push the lead back to 84-70.
Long Island again got within 10 points at 97-87, but Carolina made enough free throws down the stretch to prevail.