The Pacers took an 81-72 lead on a 3-pointer by Paul George and then went scoreless for the final 4:40.
Avery Bradley created an 81-81 tie with a layup that came with 1:25 remaining. David West missed a jumper for Indiana with 1:11 to go and Roy Hibbert also misfired with 28 seconds left, giving the Celtics a chance for the final shot of regulation.
That shot came from Green, who made only 5-of-14 from the field. The comeback gave Boston its fourth straight win.
Indiana, which managed just 13 points in the final quarter, was led by George's 16 points. David West had 11 points and 16 rebounds.
It was only the second loss for the Pacers in nine games.