Holberton's two run-single provided an early lead for the Tar Heels (53-8), the top overall seed in the NCAA tournament. Canisius (42-16) trailed 4-3 in the eighth before UNC added two runs on Mike Zolk's sacrifice fly and Frank's single to stay in control.
The Tar Heels improved to 27-5 as an NCAA host, though this is the first time UNC has been the No. 1 overall seed.
"We're the No. 1 team, we're the No. 1 seed, we've got that target on our back and everybody's going to give us their best shot," Frank said. "There comes a little pressure with that, but this team's been solid all year and we stepped up to the challenge."
Benton Moss allowed six hits and three runs in just 4 1/3 innings. Reliever Chris McCue (7-1) got the win with 2 2/3 scoreless innings, while Trent Thornton got the Tar Heels out of their biggest jam in the eighth after Canisius had loaded the bases with one out in a 4-3 game.
"They gave us all we could handle," UNC coach Mike Fox said. "We just grinded out a win."
Ryan Coppinger and Jose Torralba each had two hits for fourth-seeded Canisius, which saw Thornton end its eighth-inning rally by striking out two straight batters to end the inning.
Garrett Cortright (11-4) took the loss by allowing six runs and 13 hits in seven innings, while the Golden Griffins stranded 14 men on base in their first NCAA game.
"I thought our guys showed up, they played their hearts out," Canisius coach Mike McRae said. "A pitch here, an at-bat there, a play there, a call there, and maybe we're talking about a different ballgame."
North Carolina will face third-seeded Towson on Saturday at 6 p.m. after second-seeded Florida Atlantic and Canisius meet in an elimination game at 1 p.m.