Celtics forward Jayson Tatum, left, celebrates with forward Grant Williams during Boston’s 109-81 win over the Milwaukee Bucks in Game 7 of their Eastern Conference semifinal series on Sunday in Boston. Steven Senne/Associated Press

BOSTON — In the fog of the Celtics’ Game 5 loss to Milwaukee that dropped his team into a 3-2 series hole, Boston Coach Ime Udoka made a prediction.

“It’ll make it sweeter when we bounce back,” he said.

Two wins later, the Celtics turned their coach’s prophecy into reality.

Grant Williams scored a career-high 27 points and hit seven 3-pointers, Jayson Tatum added 23 and Boston set a Game 7 record with 22 3-pointers to eliminate the NBA champion Bucks 109-81 on Sunday in the Eastern Conference semifinals.

The Celtics will face top-seeded Miami beginning Tuesday in a rematch of the 2020 East finals. The Heat beat the Celtics in six games in that series at Walt Disney World.

Tatum said his team embraced the “backs against the wall” moments it faced in having to win the final two games after their late collapse in their previous home game.

“As much as it hurt to lose Game 5, I was looking forward to that challenge,” Tatum said. “I believe in myself, I believe in this team. I expected to play the way I did and for us to respond the way we did.”

The Celtics trailed early in Game 7 before outscoring the Bucks 61- 38 in the second half to cruise to the victory. Boston used a whopping 54-point advantage from behind the arc to improve to 25-9 in decisive seventh games.

The Bucks are now 3-9 in Game 7s. They went 4 for 33 (12.1%) from the 3-point line. That’s the second-worst 3-point percentage in a playoff game ever (minimum 30 attempts).

Williams was timid early, missing 5 of his first 7 3-point attempts. It was a pep talk he got from Jaylen Brown during a timeout after Williams passed on an open shot that changed his mindset.

“For me it was like, they’re encouraging it, I might as well take advantage,” Williams said. “Each one as time got on got more comfortable.”

Williams finished 7 for 18 behind the arc. The Celtics were 22 for 55.

It helped silence another relentless night from Bucks star Giannis Antetokounmpo, who had 25 points, 20 rebounds and nine assists. But he was just 3 of 11 in the paint in the second half, including 1 for 6 the fourth quarter.

“Shots that I usually make wasn’t going in. That’s basketball. That’s sports,” Antetokounmpo said. “Sometimes you win. Sometimes you lose. There’s a winner. There’s a loser. You’ve just got to live with it.”

Jrue Holiday added 21 points and eight assists. Brook Lopez finished with 15 points and 10 rebounds.

Boston started the second half on an 11-4 run to open a 59-47 lead.

It was 63-53 when Tatum went to the bench after being whistled for his fourth foul. But the Celtics rallied without him, outscoring the Bucks 16-11 the rest of the quarter to take a 79-64 lead to the fourth.

Udoka said he’s mostly been able to maintain tunnel vision throughout his first season as a head coach, but said he allowed himself to take in the roar of the TD Garden crowd in the closing seconds.

He said being able to have Game 7 at home mattered. The Celtics won on the final day of the regular season to earn it for this matchup when the Bucks rested their regulars and were blown out 133-115 by Cleveland.

“This is what we played for, why we played the season out, to have home-court advantage in a Game 7,” Udoka said. “If you believe in the basketball gods, those things matter.”

Brown said their coach has been the catalyst to put them in this position.

“We didn’t want it to be over. We didn’t overcome all the stuff we did during the regular season for that to be it. .. At the end of the day, we wanted to come out, leave it all out there. I think we did.”

NO WILLIAMS

Celtics center Robert Williams III was available to play after missing three straight games with soreness and a bone bruise in his surgically repaired left knee. But he didn’t play.