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The chants started with just under four minutes left, as the Celtics’ emphatic 112-96 Game 7 playoff win over the Bucks shifted from a contest to a coronation. They started in one small pocket of the TD Garden, and then they spread quickly and loudly, as the fans looked ahead to what’s next.

“We want Philly!” they shouted.

Just four days ago, as the 76ers closed out their opening-round series against the Heat, their fans had belted out a similar mantra about Boston. And now, both sides will get exactly what they want, and it will come suddenly.

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The Celtics and 76ers, perhaps the two teams best positioned to be atop the Eastern Conference for years to come, will meet in the conference semifinals, with Game 1 being held at the Garden on Monday night.

This now-completed series against the Bucks was well-played and at times intense, but it always seemed to be missing something, and the matchup against the 76ers should quickly show everyone what it was.

“They’re doing something really special over there in Philly,” Celtics forward Marcus Morris said of a 76ers team that has won 20 of its past 21 games. “But so are we in Boston.”

Related: Al Horford’s value to the Celtics? Game 7 vs. Bucks is Exhibit A

When the Celtics’ locker room was opened to reporters after the game, it was not easy to tell whether the team had just won a playoff series or lost a random December regular-season game against the Magic. There was no celebrating, or even laughing and joking. It felt like a team that was mostly focused on something more.

“Our confidence is there,” said point guard Terry Rozier, who poured in 26 points. “Just have to take care of business.”

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The Celtics entered this series against seventh-seeded Milwaukee as the favorites, but because Kyrie Irving was sidelined, no one really knew the extent of their advantage. They were not perfect, but they won 55 games and secured homecourt advantage so they would not have to be.

The home team won all seven games in this series, just like in Boston’s conference semifinals matchup against the Wizards last season. And the Celtics will have homecourt advantage against the 76ers, too.

This team has been ravaged by injuries, though, and now it has one more to deal with. Forward Jaylen Brown, who had been Boston’s best offensive player in this series, left Saturday’s game with a strained hamstring in the second quarter and did not return.

Related: Notebook: Jaylen Brown is dealing with hamstring strain

The encouraging news was that he was available to come back into the game, but coach Brad Stevens did not need him to. Brown said afterward that he had suffered a grade-1 strain. He said he will get an MRI on Sunday, but added that he intended to be ready to play by Monday.

“Whatever it takes,” he said, “because I wouldn’t miss this next series for the world.”

The Celtics led, 48-36, when Brown departed and outscored the Bucks, 64-60, without him. Al Horford had 26 points and eight rebounds and seemed to provide key baskets whenever Milwaukee mounted a charge.

“End of the first half start of the second was where we looked a little big lethargic,” Stevens said, “and when we came back to the huddle for the first timeout, we had actually increased our lead by 2 and it was largely due to [Horford].”

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Jayson Tatum added 20 points for the Celtics, who made 53.6 percent of their shots overall.

Khris Middleton closed out a phenomenal series for the Bucks with 32 points. Butsuperstar forward Giannis Antetokounmpo was held to 22 points on 7-of-17 shooting, and Milwaukee was outscored by 16 points during his 41 minutes on the floor. For the third consecutive game, Stevens started rookie forward Semi Ojeleye, almost solely to slow Antetokounmpo, and he was up to the task.

Related: Gasper: After that Game 7, Eric Bledsoe definitely knows who Terry Rozier is now

“We just tried to do our best,” Stevens said. “I thought the team effort on him was outstanding, led by Semi. I thought he was unbelievable in these three games defensively.”

In Game 6, the Bucks destroyed Boston in transition. But in Game 7, the Bucks were held without a fast-break point. The Celtics’ shot-making and 11 offensive rebounds played a large role, but so did an aggressive defense that swarmed into the paint to thwart easy chances.

After the game, Morris was stunned to find out that the figure was so low.

“Zero?” he said. “Damn. I didn’t know that. We did a great job of sticking with the game plan. Damn, zero? We did a good job I guess.”

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The Bucks took an early 15-10 lead Saturday, but after Morris and Marcus Smart entered the game midway through the opening quarter, Milwaukee missed six consecutive shots and turned the ball over three times during a fierce 15-0 Boston run.

The only field goal Milwaukee made during that flurry came at the wrong end, as Antetokounmpo inadvertently tipped in a Celtics basket.

With 7:01 left in the second quarter Bucks points guard Eric Bledsoe went to the bench with his third foul, and 90 seconds later Antetokounmpo collected his third and joined him there.

The Celtics’ lead stood at 41-30 then, and it seemed like a perfect opportunity to deliver a crushing blow. Instead, Milwaukee outscored Boston by 3 points over the rest of the half, and Boston the Celtics were left to push forward without Brown.

But Horford had steadied them several times, including when he answered an 11-0 second-quarter Bucks run with a pair of baskets.

The Bucks started the third quarter quickly, as Bledsoe hit a 3-pointer and a layup to pull his team within 54-51 with 9:33 left, but Horford once again had an answer. He had the ball stripped away in the post, but he instantly ripped it back and scored inside with 7:05 left. Then 30 seconds later Smart lofted an alley-oop that Horford threw down with two hands, helping stretch the lead back to 65-55.

Morris and Tatum hit back-to-back 3-pointers in the final 90 seconds to stretch Boston’s lead to 81-65, and the advantage would not dip below 11 points again.

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“When we came in today,” Rozier said, “I knew we were ready to play.”

Related: Antetokounmpo: ‘Guys were just in my face’


Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him on Twitter @adamhimmelsbach.