Still, amid the career highs and gaudy numbers, there was just enough sloppiness, turnovers and bad 3-point shooting for North Carolina coach Roy Williams to have concerns in the school's return to the NCAA tournament.
Zeller scored 32 points, Henson added 28 points and six blocks, Barnes had 24 points and 16 rebounds and North Carolina used its hulking size to mask other problems in a 102-87 victory over scrappy Long Island University on Friday night in the East Regional.
"Am I pleased about the win? You're darn right," Williams said. "Am I pleased about some of the turnovers? Not at all. Am I pleased about going 3-for-17 from the 3-point line? Not at all. But we have to build on this to be ready to play better in the next game."
And Williams was quick to point out it was good to be back on this stage.
After winning the 2009 NCAA title, North Carolina was relegated to the NIT a year ago in a season that ended with 17 losses. It wasn't as easy as expected by many, but the second-seeded Tar Heels (27-7) eventually wore down the 15th-seeded Blackbirds (27-6) thanks to their big men.
The 7-footer Zeller and 6-10 Henson kept catching high passes for easy layups over smaller LIU to each record career highs in points. They combined to hit 22 of 29 free throws. Henson, who was hitting 47 percent of his foul shots, went 8-for-10.
"We had mismatches inside so we just kept throwing it inside and I got lucky and made some shots," Zeller said.
Julian Boyd had 18 points and 12 rebounds, C.J. Garner added 16 points and Jamal Olasewere scored 15 for LIU, which faded after rallying to tie with under 5 minutes left in the first half as its nation-best 13-game winning streak was snapped.
"We don't see size like that. I don't think there are many teams in the country that are that long," LIU coach Jim Ferry said. "We're a team that goes inside a lot and gets fouled, but they had 10 blocked shots. We're just not used to that."
Still, North Carolina was far from sharp despite playing a virtual home game 2½ hours from campus.
There was a meltdown in the first half and another hiccup midway through the second when the Tar Heels' 21-point lead was sliced to 10.
"I think it's one of those things that nobody has played significant minutes in the [NCAA] tournament," said Zeller, one of only two players left from the 2009 team. "It's one of those things that when you get up by 10 or 15 in a regular-season game they might just go away, but it's their last game and they're going to keep coming back."
LIU, which came in as the nation's fourth-highest scoring team at 82.6 points a game, didn't shy away from running with the equally fast-paced Tar Heels. But North Carolina's overwhelming talent was the difference in its 24th consecutive NCAA tournament win in its home state.
The Tar Heels, who overcame 18 turnovers with 51 percent shooting from the field, will play the Washington-Georgia winner Sunday.
The Blackbirds, the Northeast Conference champions making their first NCAA appearance since 1997, fell to 0-4 in the tournament despite a decent showing in a difficult environment.
"I hope we did prove something," Olasewere said. "We went out there and played as hard as we could, and we gave North Carolina a fight with them being an ACC team and a No. 2 seed. I think we proved a lot even though we lost."
And LIU's 3-minute stretch of flawless basketball in the first half briefly had their small, but loud, fan contingent dreaming.
After falling behind 12-2 and 31-19, the Blackbirds suddenly got their high-scoring offense going. As North Carolina went on a turnover spree, Olasewere was scoring off the dribble, Boyd knocked down a 3-pointer and Ferry was doing a triple-fist pump in a 12-0 run to tie it.
But the Blackbirds, who entered with a nation-best 13 road victories, had no answer for North Carolina's big men.
Henson surpassed his career high by halftime with 20 points, and Barnes' late scoring spurt put the Tar Heels up 53-42 at the break even as Williams fumed, punching a chair after North Carolina's 11th turnover of the half.
The Tar Heels' 7-0 run to start the second half put it out of reach. Henson, whose previous career high was 19 points, later scored six straight points to make it 66-45 with 16:47 left.
Zeller had his way inside in the second half against an LIU team whose tallest starter was 6-7, scoring 25 points. Kendall Marshall added 10 assists in North Carolina's 15th win in 17 games.
The Tar Heels know, however, that things will get tougher.
"We made some crucial mistakes," Zeller said. "Those are mistakes we can't make in the further rounds."