Indiana led 83-69 before Atlanta started the comeback. Korver hit back-to-back 3-pointers and added another jumper, cutting the lead to 83-82.
Korver then missed another jumper but Josh Smith grabbed the rebound and passed to Jeff Teague, who hit a 3-pointer with 1:04 remaining to give Atlanta an 85-83 lead. Teague added another basket to cap the 18-0 run.
Lance Stephenson ended Indiana's drought by hitting a 3-pointer with 21 seconds remaining, cutting Atlanta's lead to one point. Lou Williams answered with a quick basket for the Hawks.
Paul George missed a last-second 3-pointer for Indiana.
David West and George Hill each scored 20 for the Pacers.
The Pacers announced earlier Wednesday that forward Danny Granger is expected to miss up to three months after receiving an injection in his left knee to treat patellar tendinosis. Granger, who hasn't played this season, averaged 18.7 points to lead Indiana last season.
Al Horford had 16 points and Teague had 15 for Atlanta, which outscored Indiana 24-9 in the final period. Korver scored 13 points.
Atlanta's 18-0 run matched the 18 unanswered points by the Pacers in the third period, when they appeared to take control of the game.
The Hawks led 62-56 before going scoreless for more than 6 minutes, missing nine straight shots from the field, as Indiana built its lead. Atlanta's Josh Smith and Zaza Pachulia were called for technical fouls during the run.
Hawks coach Larry Drew tried a big lineup in hopes of matching up against Indiana's 7-foot-2 Roy Hibbert and the 6-9 West inside. Pachulia, normally a backup, started at center as Horford shifted to power forward. Smith moved from power forward to small forward. Atlanta also went bigger in its backup with Korver at shooting guard.
The added size made little difference early as West had 12 points in the first quarter.
Indiana led 25-22 after the period, but Atlanta opened the second with a 15-2 run for a 37-25 lead. The Pacers answered with a 10-0 run later in the period, and the Hawks led 51-50 at halftime.
NOTES: Pacers F-C Jeff Pendergraph (concussion) was inactive. ... Drew said C Johan Petro, who has been held out with lower back pain, will remain inactive until he can log enough practice time to feel comfortable in games. ... Smith missed four straight free throws in the opening minutes of the second half.