The Heat won the series 4-1, and will meet Indiana in the East semifinals starting Sunday in Miami.
"We do not take this for granted," Heat coach Erik Spoelstra said. "This was a tough series. We feel very good about moving on and it'll only get tougher from here."
For the Heat, it was only the first step. The reigning East champions have one goal - getting back to the finals and winning it all - and that was likely why even beating the franchise's longtime rival prompted, at most, a subdued celebration.
"We will savor this win tonight," James said. "And then we get to work tomorrow and get ready for Indiana."
Anthony scored 35 points for the Knicks, including a spinning jumper over James at the end of the third quarter that pulled New York within 81-67. It was far from being enough to stave off an all-too-familiar playoff result for Anthony, part of that 2003 draft class that also yielded James, Bosh and Wade.
Anthony has played 54 postseason games, being part of wins only 17 times. A misleading stat for certain - it's hardly all on him - and no shortage of people in the Heat organization interrupted their celebrating of a series-clincher to tip their caps Anthony's way afterward.
"We fought, under the circumstances," Anthony said. "I'm not one to make any excuses for anything . . . But Miami, they're a tough defensive team. They stick to what their schemes are."
In another game:
* At Memphis, Marc Gasol had 23 points to help the Grizzlies stave off elimination with a 92-80 win over the Los Angeles Clippers, who lead the series, 3-2.