"We were down Paul, down so many bodies," Scott said. "It was great for everyone to come out and play and finally get a win."
New York has lost two straight and seven of nine to fall 5½ games behind Atlanta for the eighth and final Eastern Conference playoff spot.
Atlanta began the game without Millsap, who sustained a right knee contusion late in Friday's loss at Detroit, but the Hawks rallied from a 17-point deficit to take a 74-73 lead on Lou Williams' 3-pointer early in the fourth.
The Hawks, who finished 16 for 31 beyond the arc, never trailed again.
"It feels so good," Teague said. "You work hard every day. We come in here and compete. We just couldn't get over the jump the last couple of games. To get one under our belt made us feel really good."
New York coach Mike Woodson said before the game that the Knicks were preparing to buy out the contracts of veterans Metta World Peace and Beno Udrih. Neither made the trip to Atlanta, but Anthony indicated the team's problems are bigger than one or two players.
"It's same things, different days," Anthony said. "It's starting to get tough to handle. It's definitely tested me. The frustration has definitely sunk in."
Scott scored nine straight points to put the Hawks up 33-23 in the second, but New York went on a 33-6 run to take a 56-39 lead on Raymond Felton's long jumper early in the third.
Anthony grabbed a rebound midway through the third, dribbled up the court and hit a 3 from the right wing to make it 63-48. He and Hawks guard DeMarre Carroll were called for a double technical foul on Atlanta's ensuing possession and Woodson, who was defending Anthony to official Ed Malloy, was called for a technical, too.
"I think the biggest thing is a lot of people get caught up in me and Carmelo trash talking, but I think it was bigger than Carmelo tonight," said Carroll, who finished with a season-high 24 points. "Coach (Mike Budenholzer) told me that you've got to learn how to get your guys motivated. If I've got to talk to our guys to get Jeff Teague scoring (eight) in a row and Mike knocking down 3s and Lou, that's why I've got to do."
The Knicks, who lost in double-overtime Friday at Orlando, fell into another defensive lapse on the perimeter from the closing seconds of the third through the first two-plus minutes of the fourth.
Williams began the game 0 for 7 from the field, but hit three straight 3s, and Hawks also got one trey from Scott and Teague to take an 80-75 lead.
"We have leads, we have opportunities to win the ball game and down the stretch we get in close games," Chandler said. "Whenever you give up 39 points in the fourth quarter, it's going to be difficult for you to win."
Scott's previous career high was 23 points at New York last April 17.
Elton Brand, the Hawks' 15th-year center, played a team-high 43 minutes, finishing with one point and six rebounds. Another starter, guard Shelvin Mack, finished with just three points after going 1 for 9 from the field.
Atlanta outscored the Knicks by 17 points at the free throw line.
It seems as nothing is going right for New York.
"I'm going to keep coaching and I'm going to keep pushing," Woodson said. "If it means being naggy or whatever, that's my job. But I've got to get them over the hump, man. I've got to get them over this funk that we're in."
Former Atlanta and New York coach Lenny Wilkens, 76, was honored at halftime by the Hawks 20 years after he led the team to its most recent division title in 1993-94. Wilkens, who last coached in 2004-05, was joined on the court by longtime friend and former teammate Paul Silas, former Hawks center Dikembe Mutombo and Atlanta general manager Danny Ferry, who played for Wilkens in Cleveland. .... Kyle Korver hit first 3-point attempt, extending his NBA record to 124 straight games with a trey. ... With Millsap injured, the Hawks requested waivers on G Jared Cunningham and signed C Dexter Pittman to a 10-day contract. Pittman did not play.