The Thunder trailed 33-24 after the first quarter and would have been in more serious trouble had it not outscored Denver 12-0 at the free-throw line.
OKC made its first nine shots of the second quarter to pull within 48-45 on Nick Collison's dunk halfway through the period.
The Nuggets extended their lead again, but sparked by the tremendous all-around play of Westbrook, the Thunder closed out the half with a 10-2 run to trail 60-59 at intermission.
OKC took its first lead of the game in the third quarter and was sparked by Durant, who had 14 points and went 3 for 3 from 3-point range in the period.
Denver battled back from an eight-point fourth-quarter deficit to regain the lead in a contest that featured nine ties and nine lead changes.
The Nuggets were hurt by poor free-throw shooting, converting 21 of 33 (.636).