CHAPEL HILL — To hear Roy Williams tell it, he was lucky to have a team to put on the floor Tuesday night. There were players throwing up in practice and others getting fluids at the hospital and James Michael McAdoo nursing a sore back and at least one doing more running back and forth to the bathroom than up and down the court.

“I think it’s just kind of going through our team right now,” Williams said Monday, not knowing who was going to be healthy enough to play against Wake Forest. They all did, not entirely surprisingly, even P.J. Hairston, who was dealing with not only the flu but the concussion he suffered last Tuesday after colliding with teammate Dexter Strickland.

Still, for the Tar Heels, this was an important step, even against a Wake Forest team that remained winless on the road in the ACC after the 87-62 loss.

Wake Forest may be the flu vaccine of opponents, but the Tar Heels did as much to heal themselves, getting to the free-throw line, turning the Deacons’ many YMCA-level turnovers into fast-break baskets and taking – and making – smart 3-pointers.

Whatever issues North Carolina might have had, they weren’t apparent Tuesday.

All teams go through these stretches, where the accumulation of bumps and bruises adds up and some malevolent strain of the Hong Kong pigeon flu or the Down Under norovirus has half the team filling up the wrong kind of bucket. The Tar Heels didn’t just survive. They dominated.

They closed the first half on a 15-1 run and never looked back. McAdoo used his aching back to drag Wake Forest’s forwards around the court all night, going over and around them at will. Only his erratic free-throw shooting kept him from scoring more than 20 points and beating out Reggie Bullock’s 23, and neither of Hairston’s ailments seemed to slow him.

Typically, these things tend to trickle out afterward, but once Williams started going over Hairston’s issues Monday, he couldn’t help himself from going through the whole list. That advance knowledge made Tuesday a sort of public referendum on handling adversity – one the Tar Heels won, easily.

It will get tougher for North Carolina when the Tar Heels, now 6-3 in the ACC, head to league-leading Miami on Saturday, but it’s hard to imagine any better preparation than this. They might not have played their best, but they might also not be far off.

“We’re still right around the corner from it,” Bullock said. “The game today, we had great stretches and we had some stretches where we could have done better. Once we can put a whole game together, we’ll be a Top 25, Top 10 team in the country.”

With that continual improvement since the back-to-back losses to Virginia and Miami to open the ACC schedule, it’s fair to ask: Would they have fared so well under these circumstances earlier this season?

It’s a tough question to answer, in part because the Deacons had no answer for McAdoo and, in fellow freshman Codi Miller-McIntyre, point guard Marcus Paige had a matchup he could win handily. And in part because, with Hairston back, the Tar Heels had their full roster available for the first time in 2013 and only the fifth time in the past 15 games.

“I think we are a little more mature and experienced,” Williams said, “but it does help us to have everybody available, too.”

Wake Forest’s performance was a tonic that could cure all ills, but the Tar Heels also showed just how far they have come. It might not have been easy, but it sure looked that way.

DeCock: ldecock@newsobserver.com, @LukeDeCock, 919-829-8947