The Heat will meet Indiana in the East semifinals starting Sunday in Miami.
Carmelo Anthony scored 35 points for the Knicks, including a jumper at the end of the third quarter that pulled New York within 81-67.
Amare Stoudemire scored 14 points, Landry Fields and J.R. Smith both added 12 and Tyson Chandler grabbed 11 rebounds for New York.
Stoudemire fouled out with 4:48 left, and the Knicks cut the lead to 11 points four times in a 2-minute span. Miami answered every time, the last of those a 3-pointer by Shane Battier with 54 seconds left.
The last time New York advanced in the post-season came at Miami's expense in the East semifinals in 2000.
GRIZZLIES 92, CLIPPERS 80
MEMPHIS, Tenn. (AP) — Marc Gasol scored 23 points and Zach Randolph added 19 as Memphis avoided elimination and forced a Game 6 in the Western Conference first-round series.
Game 6 is Friday night in Los Angeles.
Rudy Gay added 14 points for Memphis.
Mo Williams had 20 points for the Clippers while Chris Paul scored 19 and Blake Griffin had 15 points and 11 rebounds. Paul and Griffin both missed time in the fourth quarter with injuries.
Paul strained his right hip flexor and appeared to jam a finger while Griffin hyperextended his left knee.
Memphis, which blew a 27-point lead in Game 1, was up 24 with 3 minutes left in the third quarter. Randy Foye pulled the Clippers within 85-79 on a layup with 55.7 seconds left but that was as close as they would get.
The Grizzlies outscored Los Angeles 48-26 in the paint and had a 42-35 edge in rebounds.