The Knicks improved to 22-21, the first time they've been over .500 since Dec. 2. They have won five of six, but began the night in 10th place in the Eastern Conference.
"It's a great team win," Barrett said. "They really fought back, but a number of us made plays down the stretch. It was fun to watch. (Randle) played great tonight. He really got going in that second quarter and carried it through tonight big time.
"It feels good for sure, but that's what we're working for. We had a tough month (of December), but it's starting to pick up now. It's fun to be a part of."
Trae Young led Atlanta with 29 points, and Danilo Gallinari had 17. The Hawks have dropped five straight and nine of 11 to fall to 17-26. They began the night 12th in the East.
Atlanta, which knocked off New York in the quarterfinal round of the playoffs last year and advanced to the conference finals, has lost 10 straight at home.
"We were tired, but they were tired as well," Hawks coach Nate McMillan said. "If you're taking quick shots as we did, you're bailing the defense out. They don't have to guard. You've got to understand time, score and situation and do a better job of managing getting what you want in that offensive set and not settling for something quick, trying to get everything back quickly.
"We took some quick shots, and the lead ballooned to (17). All of a sudden they have momenum and control of the game."
Lou Williams' jumper pulled Atlanta within four at the 8:35 mark of the fourth and Williams followed over a minute later with a 3 that made it 93-91, but that was as close as the Hawks would get before New York's Evan Fournier drilled a 3 and hit a layup to push the lead to six.
Barrett followed with a 3 and Randle hit a layup that made it 108-100 with 2:51 to play. Fournier's 3 made it 111-100 before Mitchell Robinson's dunk gave New York a 13-point lead that ended the suspense with 1:47 remaining.
Knicks coach Tom Thibodeau was impressed with Randle's nine assists and the rest of his team's ball movement.
"I thought Julius made great reads all game long," Thibodeau said. "That got us going, and you can't say enough about the way RJ is playing also. When those guys are aggressive like that, it opens things up. I thought the rebounding was a big factor. Defense in the first half was really good."
The Knicks led by as many as 17 in the third, but Thibodeau knew the Hawks weren't going away easily.
"We sort of got loose, and you can't do that," Thibodeau said. "You get loose against a good offensive team, which they are, and they can chop 10 points off in a minute, and they did. Then you're fighting for your life, and that's what we did."
Robinson had 14 points and 13 rebounds, and Fournier finished with 18 points.
Knicks: F Cam Reddish, acquired from the Hawks in Thursday's trade, was out with a right ankle sprain. He watched the game from the bench. ... G Kemba Walker, sidelined with a sore left knee, did not make the trip. He has not played in the last eight games. ... Reserve C Nerlens Noel was not available because of a sore left knee. ... Randle had to leave the game briefly early in the first because of a shoe malfunction.
Hawks: Dropped to 2-11 in their last 13 regular-season meetings against New York. ... G Bogdan Bogdanovich was out with right knee soreness. ... C Clint Capela missed his fourth straight game with a left ankle sprain. ... G Kevin Knox, acquired in the Reddish trade, did not play.
Knicks: Host Charlotte on Monday.
Hawks: Host Milwaukee on Monday night.
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