James had 17 points in the final period for the Heat, who held the short-handed Knicks to eight field goals in the second half and will go for the sweep Sunday afternoon.
"He just has to stay with it," Heat coach Erik Spoelstra said. "He had some turnovers, he had some mistakes but he was able to keep his head in it."
Wade added 20 points for the Heat and Mario Chalmers had 19, hitting consecutive three-pointers in the fourth quarter when the Heat finally brought some beauty to what had been an ugly game.
"My mindset was to make plays for our team to try and help us win down the stretch," James said. "I was able to come in and make some plays to help us win."
Carmelo Anthony scored 22 points but shot 7-for-23 for the Knicks, who are playing without Amare Stoudemire, Jeremy Lin and Iman Shumpert and needed a super effort from Anthony that he didn't come close to providing.
"When you can't score the basketball, that makes the game extremely hard, no matter how much defense we go down there and play," Anthony said.
The Knicks broke the record set by Memphis from 2004-06. They haven't won a playoff game since April 29, 2001, Game 3 of a best-of-five series against Toronto.
No NBA team has overcome a 3-0 deficit.
Chris Bosh had nine points and 10 rebounds hours after the birth of his first child. He flew to New York with the Heat on Wednesday, then quickly hopped on a flight back to Miami after learning his wife was in labor. He returned Thursday afternoon following the birth of his son, arriving at the arena about 30 minutes before the game.
Lin is practicing again after knee surgery but is not ready to return. Shumpert tore a knee ligament in Game 1, and Stoudemire is hoping the hand injury he sustained punching a fire extinguisher case following Game 2 is healed enough to let him play Sunday.
In another game *
At Dallas, Kevin Durant scored 31 points on 11-for-15 shooting, and the Thunder never trailed en route to a 95-79 victory over the Mavericks for a commanding 3-0 Western Conference series lead over the defending NBA champs. Game 4 is Saturday in Dallas.
Dirk Nowitzki had 17 points to lead Dallas.
Suspended Lakers forward Metta World Peace will appear on the late-night comedy show "Conan" in his first extended one-on-one interview since he elbowed the Thunder's James Harden in the head. TBS said World Peace would sit down with Conan O'Brien on Monday night. The former Ron Artest is suspended for seven games, which will carry through at least late next week. The Lakers don't have a game Monday.