The leader in attack for the Florida guys was Jimmy Butler with 35 points, while for the Celtics it was their star Jayson Tatum with 30 points.
The second game is next Friday at the same venue in Boston.
It was the third time in the last four seasons that the Celtics and the Heat met in the Eastern Conference Finals.
Miami swept the Boston team in six games in 2020 before losing to the Los Angeles Lakers in the NBA Finals.
But last season, the Celtics swept the Heat in seven games before losing to the Golden State Warriors in the championship round.
Tatum’s star was on display for history. He had a record 51 points in Game 7 as the Celtics defeated the Philadelphia 76ers 112–88 to advance to the Finals.
Boston led at halftime 66–57 with 18 points from Tatum.
The Heat erased a 13-point deficit in the second quarter, taking home-field advantage from the Celtics to take control, outscoring Boston 46–25 in the third quarter.
Tatum, who scored 30 points, committed two crucial turnovers in the final minutes as the Heat turned the defensive screws.
Butler had five rebounds, seven assists and six steals. Center Bam Adebayo had 20 points with eight sacks and five assists, and Max Strauss, Gabe Vincent, Caleb Martin and point guard Kyle Lowry each had 15 cards for Miami.
“It just shows the group of guys we have,” Butler said of a solid, balanced performance.
Butler from start to finish
Once again, Butler got off to a strong start, his 12 first-quarter points marking his seventh game of these playoffs with a double-digit first period.
It was a back-and-forth battle, however, as neither team led by more than four points in the first quarter, which featured 13 lead changes and ended with the Celtics up 30–28.
Tatum got hot in the second quarter as the Celtics extended their lead to 13 points before taking a 66–57 lead at halftime.
As Boston outscored Miami in the paint 40–16 in the first half, Marcus Smart continued his offensive run with 10 assists in the first half, tying his career high for a half.
The Heat responded with a vengeance in the third and led by 12 cards going into the final draw.
Troubled by 11 turnovers in the first half, the Heat had just one in the third quarter.
Boston opened the quarter on a 7–0 run and trailed by only four points with 2:31 remaining.
Butler hit a 3-pointer that put Miami up by 10 with 1:03 to play.
Miami made 16 of 31 3-point attempts, while the Celtics made only 10 of their 29 attempts from beyond the arc.
The Celtics will look to even up the best-of-seven series when they host Game 2 on Friday, but Butler said the Heat won’t be satisfied with leaving Boston with a split first two games.
“We did our job tonight,” Butler said. “But we have another one in two days.”
This year the Heat shook off an injury-plagued regular season by defeating the top-seeded Milwaukee Bucks in the first round to advance out of the play-ins and be seeded eighth.