The Tar Heels made 13 of 25 three-pointers to go along with a 42-21 rebounding advantage to beat the Bulldogs 103-90.

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CHAPEL HILL, N.C. — North Carolina made shot after shot, finally backing its Hall of Fame coach’s claim that he has a sharp-shooting bunch. And when they did miss, the Tar Heels relentlessly flew to the rim to pursue the ball for another chance.

Saving all that for a highly ranked opponent in a marquee nonconference game will only help with confidence, too.

Cameron Johnson had 25 points and six three-pointers to lift No. 12 UNC over No. 4 Gonzaga 103-90 on Saturday night, a strong performance for a team that had flopped in a previous measuring-stick nonconference game.

It was a few days after Thanksgiving when the Tar Heels lost at No. 5 Michigan, looking overwhelmed at both ends and leaving Roy Williams to say — among many things — that “right now we stink.”

This time, facing a team that ranked No. 1 in the AP Top 25 a week ago, the Tar Heels (8-2) shot 57 percent in the first half to build a 14-point lead at the break. And they never let the Zags closer than eight after halftime.

“I think we needed it, just to show ourselves how good we can be,” senior guard Kenny Williams said. “We see everybody talking about ‘Carolina’s defense is horrible’ and all that, so we just need to show ourselves how good we can be and the potential we could play with going deep into the season.”

UNC finished the game shooting 55 percent, including 13 of 25 from three-point range, in a matchup featuring two of the nation’s best offensive teams. Yet it was the Tar Heels’ work on the boards that proved just as important.

North Carolina finished with a 42-21 rebounding advantage. That included 14 offensive boards that led to a 27-0 edge in second-chance points, which proved critical on a night when neither team missed too often.

Zach Norvell Jr. scored 21 points to lead the Bulldogs (9-2), who shot 56 percent after halftime and 51 percent overall. But Gonzaga never recovered after falling behind by double figures in the first half and kept coming up a shot or two short of really upping the pressure on the Tar Heels to hold that margin after halftime.

“They’re right up there with anybody we’ve played,” Gonzaga coach Mark Few said. “Especially on the glass, we haven’t been beaten on the glass like that all year. And I know we certainly haven’t given up 50 percent in both halves for defensive field goal percentage. So, they’re right there.”

The Bulldogs sat at No. 1 in the AP Top 25 about a week ago, but they’ve lost two straight — though both games were serious nonconference tests. They lost a close one last weekend against No. 3 Tennessee, then fell behind early Saturday night and never could catch up against a UNC offense that looked very comfortable on its home floor.

“I think we did our job making them take tough shots, but we just didn’t come up with the rebounds,” said Josh Perkins, who had 20 points and eight assists.

“They wanted it on the boards, and defensively they went at us. They earned that win.”