"It was a play drawn up for Kevin, but Atlanta did a tremendous job in denying the ball to him," Green said, "so I just made the play."
Durant scored 29 points, Green had 15 points and 11 rebounds, and the Thunder ended the Atlanta Hawks' three-game winning streak with a 94-91 victory Monday.
Green's three-point play made it 94-88 with 12.2 seconds remaining. Dribbling from the top of the right wing, he used his right hand to dunk past Josh Smith's outstretched arms.
"Big-time play," Durant said. "If he had laid it up, Josh Smith is such a great shot-blocker, he'd stop that. That would have been a shot-clock violation."
Durant made his first 14 free-throw attempts before his 15th bounced off the rim in the final seconds. Smith called timeout in mid-air after grabbing the rebound.
Jamal Crawford, who defeated Phoenix with a buzzer-beating 3-pointer on Friday, missed a straightaway 3 as time expired.
"It shouldn't have come down to that," Crawford said. "We should've won the game earlier."
Oklahoma City improved to 15-4 against the Eastern Conference.
Joe Johnson scored 23 points for Atlanta, which had won five of six. The Hawks shot just 6 for 23 in the fourth quarter, including Crawford's 0-for-6 performance.
"It was like the rim had a lid on it," Crawford said. "The shots just wouldn't go down for us."
Durant, whose 29.1 scoring average ranks third in the NBA, didn't score 30 points for the first time in six games. He was hardly concerned, focusing instead on Oklahoma City's ability to prevent the Hawks from getting clear looks at the basket.
"Of course making shots is good, but if we can come back and get the stop, that means we're in the game," Durant said. "I think we got stops when we needed them and we scored as well. It's easy to play defense when you've got guys behind you who are going to help you out."
Though Smith's three-point play forced an 88-88 tie with 2:48 remaining, Atlanta never led after Russell Westbrook's jumper put the Thunder ahead 16-15 with 5:09 left in the first.
Smith, who finished with 18 points and 12 rebounds, but he blamed himself for failing to get better position on Green's three-point play.
"I reached in and he kind of took my balance from me," Smith said. "I had to contest the shot, but I knew [he] was going to make it because he can palm the basketball extremely well, and he had a step on me."
Johnson blamed the Hawks for lacking intensity before the game began.
"We did come out a little lackadaisical and thought we would turn it on and off," Johnson said. "In the second half, we thought we would pick it up, but we never did."
Green gave the Thunder their biggest lead at 15 when his two free throws made it 69-54 midway through the third. But it his three-point play near the end made a bigger difference.
"After [Durant] couldn't get the ball, I didn't want to force it to him," Green said. "I know I'm capable of putting the ball on the floor. I just wanted to make a play."
Thunder C Nick Collison missed the game with a mild concussion. ... Atlanta C Zaza Pachulia had four points and nine rebounds in 15 minutes after missing two games with the flu. ... Oklahoma City improved to 19-6 overall and 7-1 on the road, when leading after three quarters. ... The Hawks dropped to 3-10, including 1/3 at home, when entering the fourth with a deficit. .... Atlanta has dropped six of seven at home against the Thunder, who left Seattle and changed their name from SuperSonics before last season.