Point guard Chauncey Billups, however, was ruled out.
The Celtics won, 101-89, winning the series and completing the sweep.
Stoudemire played with a pulled back muscle in Game 3 on Friday night. He said on Saturday that he would not play in Game 4 if the pain in his back hadn't subsided by game time.
Coach Mike D'Antoni said that Stoudemire's injury responded well to treatment on Saturday night and Sunday morning.
"It's a modern medicine miracle," D'Antoni said with a laugh before Sunday's game.
Stoudemire started at power forward on Sunday afternoon.
A post on his Twitter account Sunday read: "Getting my back ready for today's game. We have to leave our hearts on the court. NYK let's go !!"
The All-Star power forward said he spent Saturday resting and getting treatment on his back. He woke up, took some Advil and declared himself ready to play.
"I feel pretty good. I am on Advil right now so it kind of disguises the pain, but I feel pretty good. Not 100 percent but feel good enough to play," Stoudemire said before the game.
He was also confident that he wouldn't expose his back to further injury.
"I feel relief knowing that the back is still getting better as I play," he said.
He later added: "I would only sit this one out if I couldn't walk."
Stoudemire originally injured his back on a dunk attempt during warm-ups prior to Game 2. He sat out of the second half of Game 2 with back spasms and was in so much pain that he had to stand during his postgame news conference. He also needed a team trainer to help him put on his socks and shoes after the game.
An MRI on Wednesday revealed that Stoudemire had a pulled back muscle. He sat out of practice Thursday, staying home in Manhattan to receive treatment on the injury.
He worked out in the pool at the Knicks' practice facility Friday morning and had to make it through a workout an hour before tipoff to be cleared to take the court.
Stoudemire started on Friday night but struggled throughout the game. He finished with seven points on 2-of-8 shooting and pulled down three rebounds in 32 minutes. He estimated that he was playing at less than 50 percent. He said on Saturday that he did not want to risk further injury by playing in Game 4.
"It has to be better. I knew last night I wasn't 100 percent. I wasn't 50 percent last night. I was pretty much in pain the whole game, from start to finish. I just don't want to further injure the injury," said Stoudemire on Saturday, who added that he was in more pain on Saturday than Friday. "We understand how bright the future is here with the organization. ... We want to continue that success out here in the next few years. So we don't want to damage anything by overdoing it."
The Knicks trailed the Celtics, 3-0 before Sunday's game, in their best-of-seven first-round series. No NBA team has ever come back from a 3-0 deficit in a seven-game series.
Billups believed things would be different if he and Stoudemire were completely healthy.
"I feel like if I could have finished Game 1, we definitely come away with that win," Billups said before tipoff on Sunday. "Game 2, you can never really say. But I feel like we could have won the series, I really do."
Toney Douglas, who suffered a right shoulder injury in the Knicks' 113-96 loss in Game 3, started on Sunday. D'Antoni didn't believe the injury would hinder Douglas. Center Ronny Turiaf played through a knee ailment.
Injuries to key players have decimated the Knicks in their first playoff appearance since 2004.
Stoudemire was particularly frustrated with his ailment because of its origin.
Stoudemire first hurt his back while dunking the ball with one hand after hitting the backboard with the other during Game 2 warm-ups, a dunk that he completes prior to every game.
He was coming off of a 28-point, 11-rebound performance in Game 1. He has averaged just 5.5 points and 4.5 rebounds in the two games since the injury.
"We felt that we had a great chance to win that game and I was totally ready to go, to dominate for the rest of the series," Stoudemire said on Saturday.
Ian Begley is a regular contributor to ESPNNewYork.com.