The Miami Heat are on their way to the N.B.A. finals, continuing one of the more improbable postseason runs in recent years. They beat the Boston Celtics on Sunday, 125-113, to win the Eastern Conference finals in six games.

In the deciding game, the Heat were led by Bam Adebayo, who scored 32 points, snatched 14 rebounds and dished five assists. Jimmy Butler added 22 points and eight assists, and Andre Iguodala provided a spark off the bench, scoring 15 points on 5 of 5 from the field.

Miami, the fifth seed in the East, will now get the chance to try to become one of the lowest-seeded teams in N.B.A. history to win the championship. In 1981, the Houston Rockets entered the playoffs with a 40-42 record, which made them the sixth seed, back when only six teams from each conference made the playoffs. They made the finals and lost to the Celtics in six games.

More than a decade later, in 1995, the Rockets won the championship after entering the playoffs with a 47-35 record, again making them the sixth seed. Four years later, the Knicks made the finals in a strike-shortened season as the eighth seed. The 1995 Rockets are the only team lower than the No. 4 seed to win a championship.

Miami not only made the finals but also did so with a dominating playoff run. The Heat swept the Indiana Pacers in the first round, then easily dispatched the top-seeded Milwaukee Bucks, who had the best record in the N.B.A., in five games. And Miami beat the Celtics in the conference finals in six. All three teams that the Heat defeated had better regular-season records than Miami. Both of Miami’s losses in the playoffs were by less than 10 points. One was in overtime.

That this Heat team made the finals was quite unexpected, even with the addition of Butler, a five-time All-Star, last summer. But Butler’s strong play and the surprising contributions of several young players on the team — Adebayo, Tyler Herro, Duncan Robinson and Kendrick Nunn — buoyed the Heat, even without the star power of other teams in the league. There were also the midseason acquisitions of the veterans Jae Crowder and Iguodala, who will now play in his sixth straight finals. Iguodala was named most valuable player of the 2014-15 finals, when he won a championship alongside Stephen Curry with the Golden State Warriors.

Herro, a 20-year-old rookie, has been an especially strong playoff performer for Miami. He routinely frustrated the Celtics during the conference finals, most notably with a 37-point performance in Game 4 off the bench. On Sunday, he scored 19 points.

That this roster has gone this far is also a feather in the cap of Pat Riley, the team president, who was tasked with rebuilding the Heat after LeBron James left in 2014 and Dwyane Wade, the longtime franchise cornerstone, retired in 2019.

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