Jayson Tatum showed he was unfazed by the Miami Heat's physicality as he logged his first career playoff triple-double in the Boston Celtics' 114-94 Game 1 victory on Sunday.

Top-seeded Boston seized the initiative in their first-round series against Miami at TD Garden, with Tatum adding 10 rebounds and 10 assists to his 23 points, leading six Celtics in double figures.

Tatum's fine performance came despite some rough treatment from the Heat, taking one huge hit from Caleb Martin while going up for a rebound in the last minute of the fourth quarter.

Martin immediately went to help Tatum up but was pushed by Boston's Jaylen Brown, with both players awarded technicals. The Miami forward later said the incident was accidental, as he received a slight nudge from Jrue Holiday before crashing into Tatum.

The five-star All-Star was soon back to his feet, though, and he later said getting hit was just part of the game. 

"It's playoff basketball, and it's a physical game against a physical team. ***'s going to happen," Tatum said. "It's probably not the last time I'm going to get hit like that in this series.

The Celtics led by as many as 34 points in the fourth quarter, with a late run from the Heat only ever bringing them as close as 14. 

Tatum hailed Boston for staying focused throughout, adding: "It's supposed to be tough. In the playoffs no game is easy. 

"There are no guaranteed wins regardless of the score, or how much time is left. We just had to respond and we did that."

Miami struggled in the absence of Jimmy Butler, and coach Erik Spoelstra accepted they were second-best, saying: "Boston controlled this game from the tip. 

"They won the big muscle areas. They definitely won the 3-point line and the majority of the areas in between."

Elsewhere on Sunday, Milwaukee Bucks star Damian Lillard scored 35 first-half points – a franchise playoff record – as they claimed a 109-94 victory over the Indiana Pacers in Game 1 of their own first-round series.

Lillard didn't score after halftime, but his lightning start ensured the Bucks were untroubled despite the absence of two-time NBA MVP Giannis Antetokounmpo, who missed out with a calf strain. 

Milwaukee built a commanding 69-42 lead by the interval and never saw their advantage drop to single digits as Khris Middleton tacked on 23 points – 15 of them in the second half.

Looking ahead to Tuesday's second game, which will also be held at the home of the third-seeded Bucks, Lillard said: "In the playoffs, it's about setting the tone.

"We're going to see this team a lot of times, and you want to establish yourself, especially on your home floor. That was my mentality, to come out and try and set the tone in that way."

Remarking on Lillard's incredible first-half performance, Milwaukee coach Doc Rivers said: "He carried us. He was unbelievable."

Over the course of four quarters, Lillard was upstaged by Indiana's Pascal Siakam, who finished with 36 points and 13 rebounds in 40 minutes on the court.

Indiana head coach Rick Carlisle, however, was unable to look beyond their miserable start to the game.

"The first half was embarrassing," Carlisle said. "We have no excuses. We've simply got to come out better. It was ugly, and we all own it."