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.
Members of Congress to keep receiving porn magazine
Rosie O'Donnell unveils nearly 50-pound weight loss