Miami’s Jimmy Butler is stopped by Boston’s Marcus Smart and Jayson Tatum in the second half of Game 1 of the NBA  Eastern Conference Finals Wednesday in Boston. Charles Krupa/Associated Press

BOSTON — Jimmy Butler scored 35 points, including 23 after halftime, and the Miami Heat rallied in the second half to beat the Boston Celtics 123-116 in Game 1 of the Eastern Conference Finals on Wednesday night.

Miami trailed by nine at the half before turning it around with a franchise playoff-record 46 points in the third and outscoring Boston 66-50 over the final two quarters. It was Butler’s fifth game with 30 or more points this postseason and he added seven assists, six steals and five rebounds.

Bam Adebayo added 20 points and eight rebounds. Kyle Lowry, Caleb Martin and Gabe Vincent and Max Strus all added 15 points apiece. The Heat went 16 of 31 from the 3-point line.

The No. 8-seeded Heat have opened all three playoff series with road victories. Game 2 is Friday in Boston.

Jayson Tatum led the Celtics with 30 points, but didn’t take a shot in the fourth quarter. Jaylen Brown finished with 22 points and nine rebounds. Malcolm Brogdon added 19 points.

The tip-off of Wednesday’s series marked the third time in four seasons that the Heat and Celtics have met in the conference finals. Boston won last year’s matchup in seven games.

Wednesday’s opener felt every bit like a continuation of that most recent meeting. Boston dominated inside early on and led by nine at halftime.

Miami took a page out of the Celtics’ book and used a 13-1 run to quickly erase that gap and then nudged back in front in the third quarter, as Butler penetrated to create opportunities for his teammates.

The Heat outscored the Celtics 46-25 in the quarter and took a 103-91 lead into the fourth, prompting a few boos from the TD Garden crowd.

Boston responded, scoring the first seven points of the final quarter before a 3-pointer by Vincent ended the run.

Miami led 114-109 with just over three minutes to play when Brogdon was fouled by Butler. But he connected on just 1 of the 2 free throws. Butler was trapped on the next Miami possession before finding Martin for a corner 3.

Tatum traveled, giving the ball back to the Heat. A Miami miss gave the ball back to Boston, but Tatum was called again for traveling.

Miami wound the shot clock down before getting a 3-pointer to rattle in with 1:03 remaining.

The Celtics let Butler get loose early and he made them pay with 12 first-quarter points.

Boston’s defense tightened in the second and Butler didn’t take another shot until the 5:45 mark, an airball resulting in a shot clock violation. His second attempt of the quarter a few minutes later had the same result. He went into intermission with 15 points.

Meanwhile, the Celtics attacked the rim, outscoring the Heat 40-16 in the paint in the opening 24 minutes – the most allowed by Miami in a half this season. Boston also held an 11-2 advantage in second-chance points.