The Thunder came back from an eight-point deficit in the fourth quarter and took the lead with 1.5 seconds left when Durant got past DeMarre Carroll and swished a jump shot.
The Hawks couldn't get off a final shot, securing Oklahoma City's eight straight win.
Durant scored 30 or more points for the 11th consecutive game, connecting on 15-of-25 from the floor -- including five from 3-point range.
Reggie Jackson added 18 points for the Thunder.
Paul Millsap led the Hawks with 23 points and eight rebounds.