The Pacers took an 83-69 lead with 6:34 to play and then collapsed down the stretch while the Hawks were scoring 18 consecutive points.
Korver had points during the run and Teague added seven, including a driving layup with 32 seconds to go that gave Atlanta an 87-83 advantage.
Indiana finally ended its scoring drought on a 3-point shot from Lance Stephenson with 21 seconds to play, after which Lou Williams delivered a dunk that put Atlanta up by three.
Paul George misfired on a 3-pointer with a second remaining that would have forced overtime.
Atlanta has won 10 in a row at home over the Pacers.
Al Horford scored 16 points to lead the Hawks, Teague had 15 and Korver contributed 13.
George and David West both had 20 points for the Pacers, who were outscored 24-9 in the fourth period. Indiana played the middle contest of a three-game road trip that concludes Friday in Minnesota.
Celebrity Families of 2014 [PHOTOS]