Jeff Teague had 23 points for Atlanta before fouling out in the first overtime. Al Horford had 24 points and 13 rebounds. Josh Smith, who opened the second overtime with a three-point play, had 17 points and 14 rebounds.
Kevin Garnett had 24 points and 10 rebounds but fouled out in the second overtime as the Celtics were left with their longest losing streak in six years. Rajon Rondo had 16 points, 11 assists and 10 rebounds for his fifth triple-double of the season.
Korver had all of his career-high eight 3-pointers in the second half, setting a franchise record, and five in the fourth quarter.
Korver’s eighth 3, with 2:26 remaining in regulation, cut Boston’s lead to 98-96. Horford’s two free throws with 1 minute remaining tied the game at 98-all to set up the first overtime.
With the game tied at 105-all in the first overtime, Courtney Lee’s steal from Horford set up Lee’s two free throws to give Boston the lead, but Smith tied the game with a jam.
Paul Pierce, who had 12 points, missed a jumper at the end of the first overtime.
The Hawks outscored the Celtics 16-4 in the second overtime.
Jeff Green had 17 points for Boston. Courtney Lee had 16 points and Avery Bradley had 14.
Boston appeared headed for a rout when it led 48-21 in the second quarter. Atlanta trailed 57-38 at halftime following a modest recovery.
The Hawks’ comeback gained strength as they outscored the Celtics 21-2 to open the second half, including a 19-0 run for a 59-all tie. Korver had three 3-pointers in the run.
There were two more ties in the third quarter, the last at 69-all, but each time the Celtics answered to prevent Atlanta from taking the lead.
Horford made two free throws less than 3 minutes into the final period to give Atlanta a 77-75 lead — its first advantage since the opening minutes.
The Hawks led 80-77 after Korver’s fifth 3-pointer, but the Celtics regained the lead on back-to-back baskets by Pierce and Courtney Lee.
The Hawks made only 4 of 23 shots while being outscored 29-10 in the first period.
Horford started after missing one game with a sore left calf, and Devin Harris had 14 points in a backup role after missing two games with a sprained left ankle.
NOTES: The Celtics’ last six-game losing streak was April 4-15, 2007 ... The 10 points were a season low for first-quarter points for the Hawks. ... Korver extended his streak of games with at least one 3-pointer to 37, the longest of career and longest active streak in the NBA. ... Hawks C Zaza Pachulia returned after missing one game with a sore right Achilles.