The Hawks are moving on.

And leaving some long-standing failures in Boston behind.

The Hawks advanced to the second-round of the Eastern Conference playoffs with a dominant 104-92 victory over the Celtics Thursday night at TD Garden. The Hawks won the best-of-seven series 4-2. They will face the Cavaliers in Game 1 on Monday in Cleveland.

The victory marks the first in a series for the Hawks over the Celtics since moving to Atlanta, ending an 0-for-7 streak of postseason failures. It was also only the Hawks’ second series win in 11 tries over the Celtics in franchise history. The only other coming was in 1958 when they won the NBA Championship in St. Louis.

There is more.

The Hawks snapped a 10-game postseason losing streak in the city of Boston, dating back to May 18, 1988.

“Tonight is just ‘Great job. Great win. Proud of their defense,’” Hawks coach Mike Budenholzer said of his post-game message. “I think they are tired of hearing from me after six games.”

The Hawks led by as many as 28 points in the series-clinching victory. It came with another balanced scoring effort. Six players finished in double figures with Paul Millsap (17 points), Al Horford (15), Kent Bazemore (15), Kyle Korver (14), Dennis Schroder (12) and Jeff Teague (11).

“We just wore them down in the games as the series went on,” Teague said. “We just forced our will on them and figured out what we could do to slow them up a little bit. We just tried to put multiple bodies in front of Isaiah (Thomas). He is the head of their team, makes everything happen for their team. We tried to make other players beat us.”

The Hawks opened a commanding lead after a 20-8 run to start the third quarter. It gave them a 20-point lead at 61-41. The Hawks would lead by as many as 22 points in the quarter as Horford scored 11 third-quarter points.

They were not done.

The Hawks used a 14-2 run in the fourth quarter to take a 28-point lead at 89-61 with 9:51 remaining.

Game over.

Series over.

The Celtics rallied in the fourth quarter to get as close as 10 points with under two minutes to play on a 25-7 run. Thomas led the Celtics with a game-high 25 points, 16 coming in the second half.

“We learned from before with this team that no lead is safe,” Horford said. “To start the third, it was important for us to get off to a good start and just keep attacking. Having that mentality of keep attacking play after play. I felt like we did that consistently in the third.”

The Hawks took advantage of some dreadful shooting by the Celtics and led 41-33 at halftime. The Celtics shot just 27.7 percent (13 of 47) while the Hawks shot 42.5 percent (17 of 40) through the first two quarters.

The Hawks led by as many as 13 points in the first half after starting the second quarter on a 14-4 run. Paul Millsap led the Hawks with eight first-half points and Tim Hardaway Jr. played 12 minutes and had seven points. The Hawks bottled up Thomas, limiting him to nine first-half points, including four straight points to end the second quarter.

“Our activity, in both those situations, you can’t go on a run unless you get stops,” Budenholzer said of the decisive runs in the third and fourth quarters. “So I thought we were making it difficult on them to score and get good looks. Everybody was rebounding and getting out and go. Everybody contributed during those runs.”

The Celtics last lead in the game with 5:37 remaining in the first quarter at 9-7.

Once the Hawks took the lead they never looked back.