Missing Iman Shumpert, Baron Davis and Jeremy Lin through injury, while Amar'e Stoudemire played with a badly cut hand, the Knicks had staved off elimination on Sunday but could not repeat the feat in Game Five in Miami.
After Sunday's loss, when Dwyane Wade missed a three-pointer on the final possession that would have closed out the series, the Heat were determined not to give the Knicks a sniff of hope on Wednesday.
LeBron James scored 29 points while Wade netted 19 as the Heat wrapped up the best-of-seven Eastern Conference series 4-1 to set up a second-round matchup with Indiana.
"They do an unbelievable job," James said of the Pacers. "We will savour this win tonight, but then get to work tomorrow and get ready for Indiana."
Carmelo Anthony, who scored 41 points in Game Four, scored 35 to lead the seventh-seeded Knicks.
In the Western Conference, the Grizzlies flirted with another second-half collapse but regained control to beat the Clippers 92-80 and narrow the series deficit to 3-2.
The Grizzlies saw a 24-point third-quarter lead trimmed to six midway through the fourth, bringing back memories of their series-opening defeat when they blew a lead of 27.
"It brought back bad memories in the back of our heads," Marc Gasol said.
"We did a better job of executing, got rebounds and made some free throws," added Gasol, who had 23 points while Zach Randolph scored 19.
The frustrated Clippers team accrued five technical fouls and Chris Paul sat out for the final minute with an aggravated groin issue.
Paul finished with 19 points and Mo Williams led the visitors with 20 off the bench.
Game Six is on Friday in Los Angeles.