Durant, the NBA's defending scoring champion, finished with 24 points in boosting Oklahoma City to its second straight victory.
The Bulls held a 72-66 lead heading into the fourth quarter, but the Thunder opened the period on a 9-1 run.
Durant started his late surge at the 3:26 mark with a jumper that gave Oklahoma City an 87-85 lead. Another outside shot from Durant put the Thunder in front 91-87 with 47 seconds left and a field goal from the baseline made it 93-89 with 20 seconds to play. He finished off his night with two foul shots with 13 seconds remaining for a 95-91 cushion.
Serge Ibaka added 21 points and nine rebounds for the Thunder and Russell Westbrook contributed 16 points and 12 assists.
Oklahoma City outshot Chicago 49 percent to 41 and missed just one of its 21 attempts from the foul line.
The Bulls were led by Luol Deng with 27 points.
'Happy' fan videos make Pharrell cry [VIDEO]
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend