Celtics forward Jayson Tatum drives the to the basket against Atlanta’s De’Andre Hunter during Game 6 of their first-round playoff series Thursday in Atlanta. Tatum had 30 points, 14 rebounds and seven assists, and Boston clinched the series with a 128-120 win. Brynn Anderson/Associated Press

ATLANTA — After letting the series go longer than it should have, Al Horford and the Boston Celtics were eager to finish off the Atlanta Hawks.

Horford made sure his former team didn’t force a Game 7.

The 36-year-old Horford hit a huge 3-pointer in a late run that carried the Celtics past the Hawks 128-120 Thursday night for a 4-2 triumph in the opening-round playoff series.

After squandering a 13-point lead in the fourth quarter of Game 5, which cost them a chance to end the series in Boston, the Celtics were determined not to wilt again.

“We talked about finishing the game,” Horford said. “I felt the last game, for the most part, we were fine. But tonight there was that sense of urgency. We understood how important it was to not extend the series.”

Down by three, Boston ripped off an 11-0 run that included three straight 3-pointers, with Horford’s big shot sandwiched around 3s from Jayson Tatum and Jaylen Brown.

Tatum capped the spurt with a dunk off a Horford miss, giving the Celtics a 121-113 lead with 2:07 remaining.

Given how close it had been all night, an eight-point lead seemed like 80 in a game that featured 22 lead changes and 15 ties.

Now, bring on Philly.

The second-seeded Celtics advanced to face the third-seeded Philadelphia 76ers, who’ve been resting since completing their four-game sweep of Brooklyn last Saturday.

Game 1 is Monday night in Boston.

Brown led the Celtics with 32 points, while Tatum had 30. Horford, who played in Atlanta from 2007-16, chipped in with 10 points, 12 rebounds two steals and three blocks.

“It was huge,” Brown said. “Al came through for us.”

After knocking down a 3 from the corner, which put the Celtics ahead to stay, Horford yapped back at an Atlanta fan who had been trash talking him from the sideline.

“I appreciated it because he got me going. He said some stuff that I wasn’t very pleased with. I took it to heart and I was able to get that shot,” Horford said. “I appreciate him for talking trash to me. Some people you can talk trash to. Talk trash to me — it’s probably not good for you.”

Marcus Smart also came up big for Boston, scoring 22 points and brilliantly running the offense down the stretch, including a drive and dish that set up Horford’s shot.

After carrying the Hawks to that improbable victory at TD Garden, Trae Young ran out of steam in the second half. He missed 12 of 13 shots over the final two quarters.

Young had 30 points and 10 assists, but he finished just 9 of 28 from the field.

Despite a largely disappointing season that included a coaching change and another first-round exit from the playoffs, Young is optimistic about the Hawks’ future.

He’s especially looking forward to a full season under Quin Snyder, who took over from Nate McMillan with 21 games left in the regular season.

“Quin is the future,” Young said. “I believe with him here, this city’s going to win a championship.”

Dejounte Murray returned to the Hawks lineup after serving a one-game suspension for bumping an official at the end of Atlanta’s Game 4 loss.

Murray seemed a bit out of sync, missing all five of his shots in the first half. He was better in the second half but still managed just 14 points.

The Hawks needed a few more to keep their season going.

“We were right there,” Snyder said.

Young forced the series back to Atlanta with a long 3-pointer that stunned the Celtics 119=117 in Boston, capping the Hawks’ comeback in the fourth quarter.

Coming off his 38-point, 13-assist effort, Young kept it going with 18 points in the first quarter.

But the Celtics finally clamped down on the Hawks star, whose heroics had forced Janet Jackson to postpone her scheduled Thursday concert until Friday to make room for Game 6.

Now, State Farm Arena is wide open for the summer.

GRANT STEPS UP

Boston forward Grant Williams didn’t even play in three of the first five games in the series.

But he got some big minutes in the clincher.

While the stat sheet didn’t show much – three points, two rebounds, one steal, one assist in 17 1/2 minutes – his teammates lauded his contribution. They also praised his professionalism for not complaining when he was planted on the bench earlier in the series.

“When his number was called, he stepped up,” Horford said. “We do not close this game if Grant doesn’t step up and play the way that he did.”

TIP-INS

Celtics: Boston finished 18 of 42 from 3-point range. Every Boston starter made at least one from long range, as did three players off the bench. … Malcom Brogdon had 17 points. … Tatum led the Celtics with 14 rebounds.

Hawks: All five Atlanta starters scored in double figures. De’Andre Hunter had 20 points, John Collins added 16 and Clint Capela finished with 10. … Onyeka Okongwu grabbed 11 rebounds.