Durant sprained his right ankle after scoring 30 points in the first half at Golden State on Dec. 18, with the Thunder going 3-3 during his absence.
Russell Westbrook was ejected late in the first half after making a contested layup, then walking over to the Suns bench and taunting them. He finished with 20 points for the Thunder.
Eric Bledsoe scored a season-high 29 points with eight assists for the Suns, who have lost two straight after a six-game winning streak. Markieff Morris and Goran Dragic had 25 and 21 point, respectively,
Durant opened the scoring of the extra session with a pair of free throws 1:24 in, giving Oklahoma City a 130-128 lead.
The Suns quickly tied it, but Anthony Morrow hit a 3-pointer and was fouled and converted the free throw to put Oklahoma City up 134-130 with 1:54 left.
Andre Roberson came up with two straight offensive rebounds on the Thunder's next set, and Durant made two free throws to extend the margin to six.
Bledsoe converted a layup, then P.J. Tucker stole the ball from Durant and followed Bledsoe's miss for a putback slam to close the gap. Serge Ibaka then missed 3-point try at the other end.
Phoenix got a couple of good looks inside in the closing seconds, but another Tucker putback was off. The ball went off Ibaka, however, with 9.5 seconds left.
Morris missed a 3-pointer on a third offensive attempt of the possession, and Roberson made 1-of-2 from the line to secure the win.
Morris capped what turned out to be a 13-3 run with a 3-pointer to give the Suns a 126-123 lead late in the fourth quarter, then Durant answered with a trey of his own with 1:24 remaining to tie it. Durant then picked up a long rebound, raced up the court and hit Reggie Jackson, who was fouled and made both free throws to help the Thunder regain the lead.
Morris' layup at the other end kept the see-saw affair going, then each team missed on their ensuing possessions. Morrow's jumper with 1.9 seconds left was off the mark and the game headed to overtime.
Oklahoma City led 30-29 after 12 minutes and brought a 64-62 lead into the locker room at half. Durant's 3-pointer staked the Thunder to a 100-94 lead entering the fourth.