Kenneth Faried had a career-high 28 points and 11 rebounds for the Nuggets, who denied the Clippers their sixth win in seven games.
DeAndre Jordan had 19 points and 12 rebounds. It was his team record 28th consecutive game with at least 10 rebounds. Jamal Crawford added 19 points for the Clippers, who fell to 0-11 on the road when trailing after the third quarter.
No more than five points separated the teams in the third quarter with the Nuggets taking an 82-81 lead into the fourth quarter when Quincy Miller stole the ball from Crawford and swept down the court for a layup, beating the buzzer.
With 3:37 left, Griffin made two free throws to put the Clippers up 107-101 but the Nuggets scored eight straight points, getting six on free throws, and went in front by two. The Clippers answered, regaining the lead on a fast-break dunk by Griffin 111-109.
Two free throws by Lawson re-tied it at 111-all with 1:21 left. Griffin made one of two from the line and Wilson Chandler made a pair and the Nuggets led 113-112 with 50.7 seconds remaining. Both the Clippers' Crawford and the Nuggets' Lawson missed jumpers before Matt Barnes connected on a go-ahead 3-pointer with 6.2 seconds remaining.
But after a timeout, the Nuggets worked the ball to Foye, who heaved a 3 with 0.9 seconds left from the top of the key for the winner.
Though the Clippers led by as many as 13 points early on, the teams battled to a 60-all tie at the half.
Barnes and Darren Collison finished consecutive fastbreaks with layups to give the Clippers a 55-46 lead with 2:46 left in the second quarter. Chandler answered with a 3-pointer that was offset by a three-point play by Griffin, who then drew a foul, his third, while guarding Foye.
Griffin spent the final couple minutes of the second quarter on the bench, during which the Nuggets closed with an 11-2 burst, including a jumper by Lawson with 29.7 seconds remaining that evened the score at the half.
NOTES: Jordan has played in 209 consecutive games, longest active streak in the NBA. ... Faried has 55 career double doubles, including 12 this season. ... Jordan has 11 double doubles in his last 15 games. ... Griffin has 23 games with at least 20 points and 10 rebounds this season.