BOSTON -- It took nearly 60 years, but the Atlanta Hawks finally found a way to beat the Boston Celtics in the playoffs.

Atlanta hadn't won a postseason series against Boston since 1958, the year they won their lone NBA title.

The Hawks had also lost 10 straight playoff games in Boston dating back to 1988 entering Thursday, including Games 3 and 4 last weekend at TD Garden.

In Game 6, the Hawks used the lessons from those losses to come away with a 104-92 victory, eliminating the Celtics on their home court.

"This is a great environment to play in," Hawks sharpshooter Kyle Korver. "They just breathe confidence into their team. We felt like we had our chances in Games 3 and 4, and just execution wasn't good and a couple mental mistakes. A couple lapses that you just can't have on the road.

"I thought tonight, until the last two minutes, we played a really great game."

Paul Millsap had 17 points and eight rebounds, Al Horford and Kent Bazemore each scored 15 points, and Korver added 14 points and nine rebounds Thursday for Atlanta, which faces the Cleveland Cavaliers in the second round beginning Monday at Quicken Loans Arena.

The Hawks lost all three meetings with the Cavaliers during the regular season by an average of 9.7 points. Cleveland also swept Atlanta when the two teams met in last season's Eastern Conference Finals.

"We just won Game 6 in Boston," Hawks head coach Mike Budenholzer said. "I don't have any thoughts about Cleveland.

"We'll start preparing -- we may actually take a second to enjoy tonight -- and at the appropriate time we'll start preparing. Our guys will be ready, I can guarantee that."

A promising season for the Celtics ended with some jekyll-and-hyde performances.

Boston won 48 games during the regular season, highlighted by a 109-106 win to snap the Golden State Warriors' NBA-record 54-game home winning streak on April 1, and won 19 of their final 22 games at home.

A pair of sluggish starts, including a seven-point first quarter in Game 2 that was the lowest for a playoff team in the shot clock era, did the Celtics in on the road, but they snapped back into form once they returned home for Games 3 and 4.

But in Game 5 in Atlanta, Boston again suffered from a lack of energy and couldn't get its mojo back in Game 6.

"We learned a lot through this playoff series, but one of the things that I learned is we've got to get better," Celtics head coach Brad Stevens said.

Isaiah Thomas had a double-double with 25 points and 10 assists Thursday to lead Boston. Jae Crowder finished with 15 points and Marcus Smart and Jonas Jerebko each added 13 for the Celtics.

Boston shot 36.2 percent (34 of 94) Thursday and was held to 38.4 percent (206 of 537) in the series.

Despite their struggles, Thomas hopes he won't be seeing too many new faces in the locker room next year.

"I'll ride with these guys until the wheels fall off," Thomas said. "This was a special group. Hopefully we can all stick together and have something special in the future."

The Hawks outscored the Celtics 39-26 in the third quarter and led 89-61 with 9:51 remaining, but the Celtics battled back to come within 96-86 on Thomas' floater with 1:48 left.

Atlanta led by as many as six points in the first quarter before ending the period up 20-17.

Thomas played the entire first quarter, but was held scoreless until a driving layup with 2:25 left in the frame.

Crowder's dunk with 4:26 left before halftime brought the crowd back to life and pulled Boston within 34-25, but the Hawks stretched the lead to 41-33 entering the break.

Millsap had eight points and five rebounds in the half for Atlanta, which led by as many as 13 in the opening half. Thomas had nine points and five assists to lead Boston.

The Celtics were limited to 27.7 percent shooting (13 of 47) in the opening half.

NOTES: Celtics G Isaiah Thomas (left ankle sprain) was in the starting lineup after leaving in the fourth quarter of Tuesday's Game 5 loss. Thomas, whose 24.0 points per game ranked sixth in the postseason through five games, aggravated the injury in Game 4. ... Boston last made three consecutive first-round exits from 1948 to 1952, the franchise's first three postseason appearances. The Celtics lost to New York in the first round of the 2012-13 playoffs and was swept by Cleveland in last year's opening round. ... The Celtics honored retired MBTA Transit Police officer Richard "Dic" Donohue with their nightly "Heroes Among Us" award. Donahue, who was critically injured during the pursuit of the Boston Marathon bombing suspects in 2013, received a standing ovation from the crowd. ... Yankees slugger Alex Rodriguez was spotted in the crowd. The Red Sox host New York for a weekend series beginning Friday.