Durant, who also had eight rebounds, made all 15 of his foul shots. He had 73 points over two games against the Celtics this season. Russell Westbrook tallied 21 points and 10 assists for the Thunder, who are in sixth place in the Western Conference, a half-game ahead of Portland and a game in front of No. 8 seed San Antonio.
Green netted 17 as Oklahoma City won for the fourth time in five contests. It was the Thunder's 46th victory of the season, doubling the team's win total from all of last season.
"In order for us to beat the best we have to continue to work," Green said. "We've been doing that each time out. This year we've been fortunate enough to play them again and we came out on top."
Rajon Rondo had 16 points, 11 assists, five boards and five steals for Boston, which dropped into fourth place in the East, a game behind Atlanta. Kevin Garnett had 18 points and nine rebounds, and Rasheed Wallace also scored 18 for the Celtics, who have lost back-to-back home games, also falling to San Antonio by 21 on Sunday.
Boston lost despite shooting 59.5 percent from the field.
"It's a human game," Boston coach Doc Rivers said. "Sometimes you're just going to play poorly. It happens. You're disappointed both ways. That doesn't happen very often; when we play well we usually win."
Garnett's alley-oop jam off a feed from Rondo gave Boston a 101-100 edge inside three minutes left, but Durant countered with two free throws to push the visitors in front for good.
Rondo then missed a jumper, and Green buried a three from the right wing.
Ray Allen converted a three-point play for Boston, but Green was perfect from nearly the same spot as before for a 108-104 Oklahoma City lead with 1:22 remaining.
Wallace missed a three-pointer, but Durant was off the mark on a jumper. Boston couldn't take advantage asPaul Pierce was bumped on the way to the basket, but no foul was called.
Westbrook missed a three-point try, but Allen couldn't hit from long range with under nine seconds to go, sealing Boston's fate.
Oklahoma City scored the final seven of the first quarter, with Durant draining a three in the final minute to give the Thunder a 30-23 lead.
It was a reversal at the end of the second with Boston netting the final seven for a 61-57 edge. It was close throughout the third, but the teams went to the fourth even at 83.
Boston had won the previous six meetings...The Celtics handed the Thunder a 105-87 setback on December 4 thanks to 23 points and eight rebounds from Garnett...Pierce had 15 points, Allen 13 and Glen Davis 10 for Boston.