Durant had 33 points, 12 rebounds and six assists, hit the tying 3-pointer late in regulation and made the go-ahead foul shots in overtime to lift the Thunder past the Wizards 106-105.
John Wall missed a driving layup attempt at the buzzer for Washington, which was seeking its third straight win.
Bradley Beal scored a career-high 34 points for the Wizards. He shot 6-for-8 on 3s, and the team went 12-of-29 from behind the arc.
Serge Ibaka had 25 points and 12 rebounds for the Thunder, which overcame a 12-point fourth-quarter deficit for the first time since the franchise moved to Oklahoma City.
"That was definitely a resilient win," coach Scott Brooks said. "It was that never-quit mentality that we've always believed in and that's what happened tonight. We just battled and battled and battled and gave ourselves a chance to win down the stretch."
Washington led for most of the second half. The Wizards were up 83-71 after a dunk by Martell Webster with 8:03 left in the fourth quarter and 92-82 with 3:26 left. But they scored only two baskets in the final three minutes, allowing Oklahoma City back in the game.
Oklahoma City, using a small lineup, closed regulation on a 14-4 run. Durant capped the burst with a straightaway 3-pointer with 13.6 seconds left.
Beal missed a running 12-footer at the buzzer while being closely guarded by Ibaka.
"That last three minutes was some of the best basketball I've seen out of us since I've been here," Durant said. "I'm very proud of how we played at the end of the game. We have to do better, but that's a good stepping stone for us."
The teams traded the lead in overtime. The Wizards led 105-102 after a driving layup by Marcin Gortat with 1:20 left. After Ibaka scored to cut Washington's lead to one point, Durant blocked a shot by Wall and streaked toward the other end before being fouled. He made both free throws for a 106-105 lead with 40.7 seconds left.
Webster missed a 3-point attempt and Reggie Jackson rebounded for the Thunder. Jackson eventually drove the lane and passed to Jeremy Lamb, who missed a 3-point attempt from the corner with 4 seconds left, giving the Wizards a final chance.
Wall inbounded to Gortat, who tossed the ball back to him. Wall drove to the basket, but two Thunder defenders forced him to take an awkward shot.
The Wizards hurt themselves by going 13 of 26 at the free throw line.
"We played extremely well," Washington coach Randy Wittman said. "I give Oklahoma City credit for coming back. They made shots. All we needed to do in the last couple minutes of regulation was make one shot and a couple of free throws and then the game would be over with. Making that run, our guys played their tails off tonight and came up short."
The Thunder rallied without All-Star guard Russell Westbrook, who was ejected, along with Washington's Nene. They shoved each other after Westbrook was called for a charging foul for running over Al Harrington with 3:19 left.
It was the second time in the game Westbrook and Nene had tangled and both times, double technical fouls were called.
Westbrook scored 13 points but went just 4 of 16 from the field. Nene had 14 points, seven rebounds and six assists.
Beal matched his previous career high of 29 points in the Wizards' win over Brooklyn on Friday before starring again Sunday.
"Bradley's coming along and being aggressive," Wittman said. "I thought he had a decent look at the end of regulation. Doesn't go in and that's the difference."
The first half featured mostly poor shooting. Oklahoma City led 42-37 at the break despite scoring just 10 points in the second quarter.
"We started off the game relaxed, like we were supposed to win this game, as if they were just going to lie down," Durant said. "We can't come out like that."
Trevor Ariza scored 15 points, Harrington and Gortat had 11 and Wall had 10 for the Wizards. Jackson came off the bench to score 12 for the Thunder.
NOTES: Oklahoma City F Nick Collison missed the game with a bruised left hip. Brooks says Collison is day to day. Oklahoma City's next game will be Wednesday at the Los Angeles Clippers. ... Wittman said he didn't know when F Chris Singleton might return from a fracture in his left foot that he sustained in mid-September. The team originally said he would be out six to eight weeks, but Wittman said Singleton hasn't practiced yet and that "it will be a little while after that" before he's able to play. ... Gabe Ikard, an all-Big 12 Conference center for Oklahoma's football team, watched from a courtside seat. ... Westbrook and Nene each were each called for their first technical fouls with 7:20 left in the third quarter after some jawing and shoving. Asked about the ejection, Westbrook answered, "Did we win?" He refused to answer other questions about the altercation with Nene.