LeBron James scored 30 points to lead Miami over Milwaukee and complete a sweep into the second round of the NBA playoffs on Sunday while Boston avoided being swept out by New York.
Defending champion Miami rolled over the Bucks 88-77 to win their Eastern Conference best-of-seven series in four games and become the first team to advance despite guard Dwyane Wade being sidelined by a knee bruise.
Wade will have time to heal. The Heat will not open the second round against Chicago or Brooklyn until Saturday at the earliest.
"The way we are playing, we don't want too much rest," James said. "We just have to continue to work our habits, get space on offense and stay tight on defense."
At Boston, Jason Terry scored the Celtics' last nine points in the final 92 seconds of overtime to lift the hosts over the Knicks 97-90 and pull Boston within 3-1 in that series, whose winner will face Atlanta or Indiana.
The Celtics forced a game five on Wednesday, although no team in NBA history has ever rallied to win a playoff series after losing the first three games.
"The spirit and heart of a champion is what kept us going," Terry said. "They made a great run at us. But we're not dead yet."
The Heat swept a series for the first time since 2005. Miami had taken 3-0 leads in the opening playoff round the past two years but failed to finish off the set in four games either time.
A Monte Ellis jumper pulled Milwaukee within 69-67 before Miami unleashed a 19-5 scoring run that included a 4-for-4 3-point shooting effort, two from beyond the arc by Ray Allen and others by Mario Chalmers and Shane Battier.
When James capped the run with a layup, the Heat enjoyed their biggest lead to that point at 88-72 and Milwaukee's fate was sealed.
"Anytime they were able to test us, we were able to withstand it," James said. "After they would make a run, we were able to counter with one of our own."
At Boston, the Knicks rallied from 20 points down in the third quarter to take the lead at 84-82, only to have Kevin Garnett equalize on a jumper for Boston to send the game into overtime.
Terry, who finished with 18 points, made a 3-pointer with 1:32 remaining in the extra five-minute session that gave Boston a 91-88 lead.
Carmelo Anthony answered with an inside jumper for the Knicks but Terry hit a fadeaway baseline jumper to put Boston ahead 93-90.
Anthony missed a 3-point attempt and Terry added two free throws and a layup to boost the Celtics' final victory margin.
"These are the moments I live for," Terry said. "It's a long series."
Paul Pierce lead Boston with 29 points while Jeff Green added 26 and Garnett had 13 points and 17 rebounds.
Anthony, who has never reached the second round of the NBA playoffs, had 36 points and Raymond Felton added 27 in a losing cause.
The Knicks were playing without NBA Sixth Man of the Year J.R. Smith, who was suspended for the game for elbowing Terry in the chin in a victory Friday.
Pierce scored 17 points on 6-of-9 shooting in the first half, his late 3-pointer part of a 12-3 run to close the second quarter that gave the Celtics a 54-35 half-time lead.
But Felton scored 16 points of 5-of-8 shooting in the third quarter, including a 3-pointer in the final second to pull the Knicks within 68-65 entering the final period.
The Knicks took their only lead of regulation time at 84-82 with 78 seconds remaining on a jumper by Felton after the Celtics went more than three minutes without scoring.