Serge Ibaka added 18 points for the defending Western Conference champions, who've won nine of 11 to go to 10-4.
Thad Young had a season-high 29 points and career-high 15 rebounds, and Evan Turner scored 26 points for Philadelphia, which has lost two in a row after winning three straight.
Trailing most of the game, the Sixers tied it at 94 on a dunk by Young off an underneath pass by Turner with 5:01 left.
The Thunder regained the lead on Westbrook's driving layup and Durant's 10-footer made it 98-94. A pair of free throws by Lavoy Allen cut it to 98-96. The teams combined for eight misses and three turnovers until Young's layup tied it at 98 with 1:36 to go.
Each team missed its next two shots and Turner deflected away an inbound pass with 3 seconds left to send it to overtime.
That's when the Thunder found their shooting touch from long range.
Durant scored Oklahoma City's first five points on two free throws and a 3-pointer. Kevin Martin nailed a 3 to extend the lead to 106-100. Westbrook's 3 made it 109-102. Thabo Sefolosha then sent the fans scattering for the exits with another 3 for a 112-104 lead with under a minute left.
The Sixers learned before the game that All-Star center Andrew Bynum is now out indefinitely. General manager Tony DiLeo said Bynum has "bilateral bone bruises and a weakened cartilage state" in his knees. Bynum's target date for returning to basketball activities has been pushed back four times, so the team has to move on without him at least for the immediate future.
The Thunder led nearly the entire first half, going ahead by 10 on a few occasions. But after Ibaka hit a long jumper to make it 42-32, the Sixers outscored Oklahoma City 17-8 to get within a point at halftime. Jason Richardson started the run with a 3-pointer and made two more during the stretch.
Durant threw down a thunderous dunk to give Oklahoma City an 85-79 lead after three quarters.
Jrue Holiday had 10 of his 13 assists in the first half for Philadelphia.