Durant scored a career-high 51 points on 19-of-28 shooting, including five in the final minute of regulation to send the game to overtime. Westbrook scored seven of his 40 points after regulation, helping the Thunder win their ninth straight at home.
Serge Ibaka posted a triple-double with 14 points, 15 rebounds and 11 blocks in the comeback victory.
Oklahoma City head coach Scott Brooks called Durant and Westbrook's effort "amazing" and added "[Ibaka] cleaned up a lot of our mistakes and protected the basket...we gave everything we had"
The Nuggets went winless on their three-game road trip despite leading by five, 111-106, following two Al Harrington free throws with 43 seconds left in regulation.
Durant began the rally by burying a three-pointer after Westbrook came away with an offensive rebound.
Lawson missed a three-pointer at the other end with 7.9 seconds left, and Daequan Cook grabbed the rebound before quickly calling timeout.
Durant tied things in the blink of an eye, as Chris Andersen gave the All-Star forward a clear path to the lane along the left side. Two dribbles later, Durant sent a two-handed flush through the hoop with 4.4 seconds remaining.
Lawson's leaner before the buzzer was off to the right, and the Thunder never trailed in the extra session.
Westbrook rattled in a three-pointer to open OT, and it was still a three- point advantage before Durant went coast-to-coast and laid in a finger roll over Lawson for a 120-115 cushion with 57.1 seconds remaining.
Afflalo gave Denver life with a three-pointer, but was blocked at the rim by Ibaka after Westbrook hit a mid-range jumper.
Durant sealed the win and his 51-point performance with two free throws, much to the delight of a raucous Chesapeake Energy Arena crowd.
The Nuggets shot 52 percent from the field in the first half and led 58-53 at the break despite Durant's 20 points.
Westbrook erupted for 14 points in the third, which ended with the score knotted at 83-all.
Harrington drained consecutive three-pointers early in the fourth, the second providing the Nuggets with a 93-84 with 8:49 showing.
Oklahoma City improved to 12-1 at home...Durant, who also grabbed eight rebounds, shot 8-of-10 from the foul line and 5-of-6 from three-point range...Westbrook handed out nine assists...Kosta Koufos scored 13 points, while fellow reserves Harrington and Andersen each had 11 for Denver...This was the Northwest Division rivals' first meeting since Oklahoma City bounced Denver from the opening round of last year's playoffs in five games.