The Miami Heat are one win away from the NBA Finals after crushing the Boston Celtics 128-102 to take a 3-0 eastern conference title series lead.

Point guard Gabe Vincent scored a career-high 29 points, Duncan Robinson added 22 while kingpin Jimmy Butler had 16 plus six assists for the eighth-seeded Heat in Sunday night's home game.

Every team in NBA history that has won the first three games of a best-of-seven has ultimately prevailed; the Heat are 8-0 in that situation.

The hosts spread their scoring around well with Caleb Martin finishing with 18 points, Bam Adebayo with 13 and Max Strus with 10.

"The rim was as big as the ocean for everybody," Adebayo said, after Miami shot at 57 per cent.

The Celtics won three times on Miami's floor on the way to winning last season's eastern conference finals but simply never had a chance in this one and basically emptied the bench for the fourth quarter.

Celtics stars Jayson Tatum Jaylen Brown had just 14 points and 12 points respectively.

Grant Williams and Payton Pritchard each had 12 for Boston. Game 4 is Tuesday in Miami.

"I just didn't have them ready to play," said Boston coach Joe Mazzulla, who has been the subject of tons of criticism in this series

Whatever it was, whether it was the starting lineup or an adjustment, I have to get them in a better place, ready to play. That's on me."

The NBA Finals start June 1, and the way things are going, that might mean the league is about to go a few days without games.

The western conference finals could end on Monday; Denver lead that series against the Los Angeles Lakers 3-0. And now, the east finals could end on Tuesday.

There's never been a season where both conference finals ended in sweeps; it happened in 1957 in the division finals immediately preceding the title series, when Boston beat Syracuse 3-0 and St. Louis beat Minneapolis 3-0.

Of all the 3-0 series leads in NBA history, this one might be the most unexpected - a No.8 seed in the Heat, a team that struggled just to get into the playoffs, a team that was less than three minutes away from being eliminated in the play-in tournament, getting past top-seeded Milwaukee in five games, then fifth-seeded New York in six, and now on the brink of denying the No.2-seeded Celtics a second consecutive conference crown.

And the Heat let Boston know how much they were enjoying this one.

Mindful that Boston's Al Horford directed a timeout signal toward the Miami bench during Game 1 when the Celtics were on a second-quarter spurt to build a comfortable lead, Butler did the same to Horford as the Heat were running away in the third quarter of Game 3.