Felton scored 27 for New York two days after their Game 3 win in Boston.
"We did our job when we came here. We got us a win," he said. "That was our goal."
The Knicks made just 28.9 percent of their shots in falling behind 54-35 at halftime. But they tied it at 74 with 7:16 left in the fourth quarter on a layup by Iman Shumpert.
"We're a veteran ballclub so we don't panic," Jason Kidd said. "We had a great opportunity and we just couldn't close the door."
Garnett expected that.
"Good teams are going to make those runs," he said. "It's deflating, but we kept fighting. We found a way to get over the hump."
After Terry put Boston ahead 91-88 in overtime, Anthony made a fadeaway shot with 1:17 remaining. Then Terry sank a 15-footer that made it 93-90 with 50 seconds remaining.
Anthony followed with an off-target 3-pointer with 21 seconds to go and Terry was fouled by Steve Novak. He made both free throws then added a layup to close out the game. It came just in time for a player who failed to score in Game 1 for the first time in 88 playoff games.
"I had every intention of trying to make an impact on the game," Terry said. "If I wasn't making shots, I wanted to get a steal, get a rebound, any little thing to keep it going. Again, I'm going to coach AAU, but I don't want to do that right now."
The Celtics showed renewed energy early after being held below 80 points in each of the first three games. They were more aggressive and more physical than they had been.
"We knew they were going to come out like that," Anthony said. "They were fighting for dear life."
With leaders such as Pierce and Garnett, the Celtics have "tremendous" pride, Terry said. "Getting swept is something that no man that's been in this league that long wants to do. It's disheartening.
"Now we have to go into a hostile environment and they're going to be trying to get it over with. They don't want to come back here, but we do."
NOTES: Garnett finished with 13 points, 17 rebounds and six assists. ... The Knicks went 7 for 30 on 3-point shots. ... Boston had just three offensive rebounds while the Knicks grabbed 16. ... The Celtics have been swept six times in the 112 playoff series in their history. ... The Knicks were 19-2 in their previous 21 games. The Celtics were 5-14 in their previous 19. ... For the Celtics, Garnett, Green and Brandon Bass each had four fouls five minutes into the third quarter. Bass committed his fifth with 5:10 left in the period and fouled out with 4:27 to go in the game. ... Anthony committed his fourth with 4:08 remaining in the third.