GLENDALE, Ariz. — Back on the East Coast it was near midnight, near the one-year anniversary, to the day, of North Carolina’s greatest heartbreak — one that united this team on a long-sought mission of redemption. It was near midnight there when the Tar Heels began celebrating here.

For the past year, they’d often spoken of their hope of reaching this point, the final Monday night of the college basketball season. Roy Williams, the UNC coach, had often spoken with tears in his eyes about how last season ended.

Now there were tears of a different kind after UNC’s 71-65 victory against Gonzaga on Monday night in the NCAA Tournament national championship game. The Tar Heels won their sixth NCAA Tournament championship in school history. Williams his third, as a head coach.

Like so many times before during this long postseason run — like against Arkansas in the second round, and against Kentucky in the South Regional semifinal, and against Oregon here on Saturday night in a national semifinal — UNC survived. Imperiled late in all those victories, it survived.

And did again here against Gonzaga, the upstart mid-major major that was attempting to break through with its first national championship. With a little less than two minutes remaining here, the Bulldogs led by two points after Nigel Williams-Goss’ jumper from near the top of the key.

Then the Tar Heels, so calm in these situations throughout the tournament, were at their best. They closed the game on an 8-0 run, taking the lead for good on Justin Jackson’s three-point play with one minute, 40 seconds remaining, and then taking a 68-65 lead on Isaiah Hicks’ one-handed runner with 22 seconds left.

It was Hicks, the senior forward, who blamed himself after UNC’s 77-74 loss against Villanova in the national championship game a season ago. He was the closest player, after all, to Kris Jenkins, who made the game-winning shot as time expired.

This time Hicks, who finished with 13 points, earned some measure of redemption. All of his teammates did, too, as did Williams. He said the defeat last season didn’t keep him up at night, that he didn’t dwell on it. But he allowed it to fuel him, as did his players.

“It’s an amazing game,” Williams said afterward during an interview with CBS. “ … Both teams played extremely hard. I don’t think either team played very well. … One of the things we had to be was tough enough, and I think we were tough enough tonight.”

Williams said he wrote that up on a board inside the Tar Heels’ locker room — the necessity of toughness. No one personified that characteristic more than Joel Berry, the junior point guard who earned Final Four Most Outstanding Player honors.

Hobbled by two injured ankles throughout the NCAA Tournament, Berry finished with 22 points. He made four 3-pointers. He had the assist, after Kennedy Meeks’ blocked shot, that led to Justin Jackson’s dunk with 12 seconds remaining.

That gave UNC a 70-65 lead. The Tar Heels could feel it then, and moments later a Gonzaga turnover all but sealed it. Eight seconds later it was over. Berry and his teammates ran around the court, finding someone to hug. Their mission was complete. They’d achieved the redemption they’d long sought.