"We easily could've hung our heads there, but we kept fighting, got some good looks and we knocked them down," he said. "The momentum switched our way, and we could just feel it. The game turned really quickly."
With four games remaining in the regular season, Atlanta increased its lead to two games over the New York Knicks for the eighth and final Eastern Conference playoff spot.
The Celtics dropped their 13th in a row on the road, breaking the franchise mark set during the final 13 games of 1978-79.
The Hawks, who never trailed after Korver hit his second straight 3-pointer to make it 93-92 with 3:09 remaining, avoided losing at home for the second straight night to a team eliminated from playoff contention.
Teague and Korver combined for 18 points, three assists, two rebounds and two steals in the fourth quarter.
"We knew we had to win," Teague said. "It was a must win for us, so we came out played with a lot of intensity in the fourth quarter."
Boston, which blew a 19-point, third-quarter lead and lost at Detroit in its most recent game on Saturday, couldn't hold a nine-point advantage with 5:44 remaining.
"In the second half we had a big lead and we let them back in it," Rondo said. "We have to get stops, and I start with myself and turning the ball over. They turned up the pressure in the fourth quarter and took us out of our offense."
The Hawks' next three games are against teams ahead of them in the East, including Saturday at home against two-time defending champion Miami.
Atlanta matched its biggest lead of the first half at 14 when Shelvin Mack hit a 3 to make it 49-35 at the 6:31 mark of the second.
But Rondo, who sat out the loss to the Pistons to rest his surgically repaired right knee, scored seven points in the last 2:34 of the second, helping Boston cut the lead to 56-51 at halftime.
Rondo had a few dazzling moments in his first game in Atlanta since tearing his anterior cruciate ligament Jan. 25, 2013, at Philips Arena.
Early in the third, Jared Sullinger stole the ball from Brand under the Atlanta basket and flipped the ball to Rondo, who bounced a pass halfway up the court that led to Jeff Green's fastbreak layup and cut the lead to 56-53.
About 6 minutes later, Rondo stole an inbound pass from Brand and hit a runner. He followed on the ensuing possession by driving on Teague and hitting a jumper in the lane to give Boston its first lead at 67-66.
The Celtics' biggest lead was nine on Rondo's two free throws with 5:44 remaining.
But Boston was outscored 19-3 over the next 4:31.
"Our defense was what really fueled it," Atlanta coach Mike Budenholzer said. "We picked up our pressure and our effort. We some turnovers and some steals that led to transition baskets, especially a couple of those transition 3s for Kyle."
Bradley played his first game after missing the past three with a strained right Achilles tendon. ... Sullinger finished with 15 points and 11 rebounds for Boston. ... Millsap has six consecutive double-doubles. ... Hawks F Pero Antic did not play because of a sore right ankle. ... Celtics F Kris Humphries did not travel after undergoing an MRI on his right knee. Coach Brad Stevens did not have an update on Humphries before the game. ... Atlanta has been outscored 40-14 on second-chance points in the past two games. ... Boston had won four of the previous five against the Hawks.