BOSTON -- When the Celtics needed their two stars the most, they both came through. Jaylen Brown got things going, and Jayson Tatum finished it off.

After Boston didn't match the physicality of the Milwaukee Bucks in Game 1 of their East semifinal series on Sunday, the Celtics came out with a much different attitude on Tuesday, controlling the game from the opening tip and leading wire-to-wire in a 109-86 victory.

"We knew we had to come out and play like our season was on the line," Brown said, "and we did that."

Brown finished with a game-high 30 points and knocked down a playoff-career-high six 3-pointers. He set the tone for the team early on as they looked to bounce back from a lackluster performance in Game 1.

"We adjusted well," Celtics coach Ime Udoka said. "We learned some things from Game 1 and felt like we knew we didn't react accordingly to the way that we're playing. Two big teams but we haven't been outmuscled like that all year. I think our guys took pride in that, took that to heart and we knew we would come out with the right effort tonight."

Leading that charge was Brown, who had a playoff-career-high 25 points in the first half. He was key as Boston opened up an 18-3 lead and never looked back.

"It's the playoffs. Survival of the fittest," Brown said. "Every game counts."

In Game 1, the Celtics made only 10 two-point field goals, a franchise low for a playoff game or a regular-season game. Udoka lamented about how the team strayed from the mid-range game. That wasn't the case on Tuesday, as Brown hit three mid-ranges early on to set the tone there.

Udoka said he spoke to Brown and Tatum about that prior to the game.

"We knew those are open," Udoka said. "You don't have to over penetrate and drive into the bigs and take the 3 only. We have two really elite mid-range shooters and we welcome those shots especially when they're back in that drop."

Celtics forward Grant Williams said he knew hours before the game started that Brown was going to have a big night.

"I saw it his eyes," Williams said. "So at the start the game, I was just like, 'All right, do you thing' and we're supporting and cheering. He established that tone and set the mark of aggression on the offensive end, not only knocking down open shots but also moving it."

While Brown was leading the charge early, Tatum took care of things late, scoring 19 of his 29 points in the second half.

Like Williams, Tatum said he knew Brown was going to be ready for a big night coming into the game. But more so, he knew his team was ready to bounce back.

"We were pissed off in how we played last game and from top to bottom we knew that we just had to play better," Tatum said. "Simple as that."

The Celtics played stellar defense all around but did a much better job of making life difficult for Bucks star Giannis Antetokounmpo. The two-time MVP had 28 points but he went 11-of-27 from the field and 5-of-9 from the line.

Bucks coach Mike Budenholzer said credit was due to the Celtics' defenders for how they guarded him throughout the night.

"The guys on him, they're solid, good, good defenders and then quite a bit of help," Budenhozer said. "That's where he's just got to see and feel it -- do we kick it and get more 3s or he's got to finish against one-on-one defense. So, I think it's a little bit of both. But Giannis, he always figures things out."

When a reporter told Antetokounmpo what Budenholzer said about figuring things out, he said "I try. I try to figure it out."

"It's the playoffs. Obviously they're going to be physical," Antetokounmpo said. "They're going to be more physical. It's not going to be a lot of fouls called, there's going to be more active, more discipline, but at the end of the day, it's the same mentality, the mindset doesn't change, you've got to keep chipping away, keep finding solutions to make the game yours. Make good plays. Find your teammates, get in the paint. No matter what they do, my mindset and the team's mindset cannot change."

Boston got things done defensively without the NBA's 2021-22 Defensive Player of the Year as Marcus Smart sat out with a right quad contusion. With three days off between Game 2 and Game 3 in Milwaukee on Saturday, the Celtics are hopeful he'll make his return to the lineup then.

Brown has been dealing with a lingering hamstring injury, and Udoka said pulling him a minute earlier than the other starters, with Boston up 99-86 with 2:51 to go, was about preserving him since he had played 38 minutes. Brown said his hamstring felt fine and that he'll be ready to go for Game 3, and that injuries are just something every player has to deal with at this point in the season.

"The only thing that matters is the playoffs," Brown said. "Everybody, we've got to do what we got to do to make sure we're ready to perform. At this time of year, everybody has nagging injuries or things that they're dealing with, so can't let that be an excuse. You got to find a way mentally and physically to overcome whatever it is and just get it done."

Brown added that this was the Celtics' first true test of the playoffs after sweeping the Brooklyn Nets in the first round and he was curious as to how the team would respond. Tatum was confident the response was going be a positive one.

"Every game isn't gonna be perfect," Tatum said. "We're playing against the defending champs. They punched in the mouth first game. I knew we were gonna be ready tonight from a competitiveness standpoint. Making adjustments from game to game, I think that's what the playoffs are about."

ESPN's Jamal Collier contributed to this report.