Jayson Tatum scored 27 points, Marcus Smart and Jaylen Brown each had 24 and the Boston Celtics dominated the first half to roll past the Miami Heat 127-102 on Thursday night and tie the Eastern Conference finals at a game apiece.

Smart was a rebound shy of a triple-double, after adding 12 assists and nine rebounds.

Grant Williams scored 19 points for Boston, which used a 17-0 run late in the first quarter — fueled by five 3-pointers in the span of six possessions — to take control. Payton Pritchard and Al Horford each had 10 for the Celtics.

Jimmy Butler had 29 points in 32 minutes for Miami, which fell to 7-1 at home in these playoffs. Gabe Vincent and Victor Oladpio each scored 14 points, and Tyler Herro added 11 for the Heat.

The Celtics — now 4-0 in these playoffs in the game immediately following a loss — made 20 shots from 3-point range to Miami’s 10. Game 3 is Saturday in Boston.

And the margin could have been worse: Boston led by as many as 34 points in the fourth, putting this game on the cusp of really good Celtics history and really bad Heat history. The Celtics’ record for biggest postseason win ever is 40, the Heat record for biggest postseason loss ever is 36, and those numbers were within reach before a meaningless Miami run over the final moments.

Boston trailed by 10 in the first quarter, then outscored Miami 60-21 over the next 18 minutes — a 39-point turnaround that wound up leading to a 70-45 halftime lead.

The 25-point halftime lead was the biggest by the Celtics in any road playoff game, topping a 22-point edge at the break at Chicago in 2009.

Brown had 11 points in the first quarter, when the Celtics went 9 for 11 from 3-point range. Tatum then had 17 points in the second and Boston kept pulling away, on a day where everything went the Celtics’ way. They learned earlier in the day that two starters — Horford (virus-related issues) and Smart (mid-foot sprain) — were cleared to play in Game 2 after missing the series opener.

“I got to get my rest, got to get my health back, got to watch and see some things and come out and execute in this game,” Smart said.

And the good news kept coming well into the night.

Butler did all he could to try and manufacture a comeback, scoring 16 points in the third quarter and getting the Heat within 17. But a 12-2 run late in the quarter by the Celtics restored a 27-point edge. The lead was 96-71 going into the fourth and the outcome was never remotely close to being in question the rest of the way.

Miami didn’t even use its starters in the fourth quarter.