Miami became the first team in the Eastern Conference to win seven games and improved to 3-2 on a six-game road trip that ends Saturday in Phoenix.
The Heat led by 13 points heading into the fourth period, but the Nuggets rallied to within one when Andre Iguodala hit two free throws with 1:37 to play.
Ray Allen then missed a 3-point attempt for the Heat, giving the Nuggets a chance to take the lead.
Danilo Gallinari wasted no time trying a 3-pointer for the Nuggets, but it came up well short and Miami raced to the other end. Cole came through with his wide open 3-point shot from the corner, giving Miami a four-point cushion that it protected down the stretch.
Andre Miller had 19 points for the Nuggets. Kenneth Faried contributed 16 points and 20 rebounds.