11:18 PM ET

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ATLANTA -- After they were hurt by the last six minutes of Game 5 on Tuesday, the Boston Celtics played that same end-of-game stretch in Thursday's Game 6 with added urgency, leading to a win that pushed them into the next round of the playoffs.

Effective defense and timely 3s from a host of Celtics in Thursday's closing moments helped Boston pull out a 128-120 win over the Atlanta Hawks at State Farm Arena. The Celtics now move on to the Eastern Conference semifinals for a matchup with the Philadelphia 76ers, who swept the Brooklyn Nets in their first-round series.

Game 1 of the semifinals is Monday in Boston.

Atlanta's season is now over.

Celtics wing Jaylen Brown, an Atlanta-area native, started Boston's late rally, burying a 25-foot 3-pointer with 4:50 remaining. Across the next two minutes, Al Horford and Jayson Tatum knocked down their own 3s for the Celtics. All three long-range shots went unanswered by the Hawks.

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Boston ended up outscoring Atlanta 18-8 in the final six minutes, one game after being outscored by the Hawks 23-8 in the same stretch of Atlanta's Game 5 win in Boston.

Brown finished with 32 points, while Tatum had 30. They became the second duo in Celtics history to each score 30-plus points in the same game multiple times in a playoff series, joining Larry Bird and Kevin McHale, who did it against the Milwaukee Bucks in the 1987 Eastern Conference semifinals.

The Celtics didn't have the cleanest start offensively Thursday. They missed 14 shots in the paint in the first half, their second-highest number of missed close-range shots in a first half all this season.

Despite those early close misses, the Celtics finished the game outscoring the Hawks in the paint 54-50.

For the Hawks, Trae Young picked right up where he left off in Game 5. Following up his 38-point performance in Boston that included the game-winning 30-foot dagger, he had 30 points in Game 6. Most of them came in the first half. Across the final 24 minutes, Young was held to a 1-for-8 showing from the field when his shots were contested.

It wasn't until nearly three minutes into the start of the third quarter that Hawks guard Dejounte Murray finally scored his first points on a midrange jumper. Although he was scoreless through halftime, Murray was still productive for Atlanta on the offensive end. The Hawks went 7-for-9 off his passes across the first two quarters.

The All-Star was back in the Hawks' starting lineup after missing Game 5 due to a one-game suspension for making contact with and being verbally abusive to an official. At the end of Game 4, a Hawks loss, Murray bumped referee Gediminas Petraitis as he walked off the floor.

When he addressed the incident two days later, Murray said "a lot" led up to the bump, including a history of feeling disrespected by the official in the years before Murray was traded to the Hawks from San Antonio.

Atlanta's night started by spotting the Celtics nine unanswered points, part of a 12-2 Boston run that prompted a quick timeout from Hawks coach Quin Snyder less than three minutes into the game.

With the loss, Atlanta's season ends, after the Hawks went 41-41 during the regular season and blew out the Miami Heat in an Eastern Conference play-in game to secure the No. 7 seed entering the playoffs. Atlanta also finished the year going 14-18 in games coached by Snyder, including the postseason.