LeBron James scored 27 for the Heat, who will try to close it out in Game 5 at home on Wednesday. Dwyane Wade had 22, but missed a three-pointer on the last possession that would have given Miami a lengthy rest before starting the second round.
Wade's errant shot set off a loud celebration from Knicks fans whose team was on the verge of getting swept for the second straight year, and third straight time.
But they got a huge lift from Stoudemire, playing with padding over his hand just six days after he punched a fire extinguisher case after a Game 2 loss in Miami. And they got a sensational effort from Anthony, who shot 15 of 29 and was one point shy of his playoff career best.
The Knicks will need a solution at point guard after Davis was carted off on a stretcher with his severe knee injury. Jeremy Lin is close to returning from knee surgery, but Iman Shumpert was lost with a torn knee ligament in Game 1.
Stoudemire had surgery Wednesday to repair a muscle in his left hand, and the Knicks had listed him as doubtful for Sunday.
The game turned into a foul-fest, with 23 called in the second period alone. Both teams shot 33 percent in the quarter, and play slowed to a glacial pace while the teams paraded to the free-throw line. Miami led, 44-38, at halftime.
But New York regrouped and surged into the lead. After making only 13 baskets in the first half, the Knicks shot 10 of 20 in the third, getting 11 points from Anthony.
Celtics blow out Hawks
Paul Pierce scored 24 points in 18 minutes, and the Celtics opened a 37-point third-quarter lead at the TD Garden in Boston before coasting to a 101-79 victory over the Atlanta Hawks to take a three-games-to-one lead in the best-of-seven series.
The Celtics can finish off the Hawks in Atlanta on Tuesday. Game 6 would be in Boston on Thursday, if necessary.
Two nights after his triple-double helped turn back the Hawks in overtime in Game 3, Rajon Rondo had 20 points and 16 assists as the Celtics got some much-needed rest for their aging and injured roster.
Josh Smith returned after missing Friday's game and had 15 points and 13 rebounds for Atlanta. Al Horford, who played for the first time in almost four months, scored 12 points.
- Associated Press