MIAMI — A week ago, the Boston Celtics beat the Miami Heat with defense. This time, they did it with offense.

Paul Pierce scored 27 points, Kevin Garnett added 24 points and nine rebounds, and the Celtics made their first eight shots of the fourth quarter to hold off the Heat 115-107 on Tuesday night.

Rajon Rondo posted double-digit assists for the 18th straight game, extending the NBA’s longest such streak in 20 years with an 18-point, 15-assist effort.

Brandon Bass added 12 points and 10 rebounds, while Avery Bradley scored 11 for the Celtics, who shot a season-high 61 percent and survived two possessions where Miami could have tied the score in the final quarter.

“We talk about it in fighting terms,” Celtics Coach Doc Rivers said.

“We told them today before the game, you’re in a boxing match, you expect to get hit. They’re going to hit you. They did and we withstood it. I thought that was important for our team.”

LeBron James finished with 36 points, seven rebounds and seven assists for Miami, which got 20 from Dwyane Wade and 18 from Mario Chalmers.

Chris Bosh finished with 13 on 5-for-13 shooting for Miami, which has gone 5-5 in its last 10 games.

The Celtics beat Miami 91-72 in Boston on April 1, a game the Heat called “unacceptable” after establishing season lows in scoring and shooting.

This one won’t sit much better with the reigning Eastern Conference champions, who ousted the Celtics in five games from last year’s playoffs and could see them in the second round of the upcoming postseason.

No team had shot better than 55 percent against the Heat this season, and Boston’s 115 points were two shy of matching a season-high against Miami.

“We left Boston feeling awful at our performance,” James said.

“I don’t feel as bad tonight. Those guys, they were locked in. Not only did they make their open shots, they made their contested shots. … When you’ve got it going like that, just tip your hat off. We tip our hat off to them tonight. They won it.”

Boston improved to 18-7 since the All-Star break, and dealt Miami a blow in the race for the No. 1 seed in the East.

The Heat fell 21/2 games behind Chicago, which played later Tuesday at home against the New York Knicks.

“It took a while,” Rondo said, “but we’re peaking at the right time.”

A layup by Wade got Miami within 108-103 with 2:22 left, before Garnett made a high-arcing jumper that dropped softly through the net, his 11th make in 14 shots.