Playing without forward Anthony Davis, who missed his third consecutive game with a strained adductor, the Pelicans (13-12) erased an early 10-point deficit by punding the ball inside to Cousins. In addition to collected 11 fouls against Nuggets big men Mason Plumlee and Kenneth Faried.
The Nuggets (13-11) were led by Gary Harris with 24 points, but they dropped to 3-9 on the road.
Cousins continued to attack the basket in the third quarter, scoring 13 points as the Pelicans widened their lead to 97-91.
The Pelicans also controlled the boards in the quarter with a 16-7 advantage, getting three offensive rebounds on one possession that ended with a Dante Cunningham layup for a 92-87 lead.
The Pelicans put the game away with a 13-0 run in a three-minute span of the fourth quarter to take a 114-96 lead with 6:38 left. Cousins finished just short of his season high with 41 points and 23 rebounds in an 114-106 road victory over Sacramento on Oct. 26.
The Pelicans led 67-66 at the half, with Cousins and Holiday scoring 19 points each. Holiday had a 12-point first quarter on 6-of-9 shooting, and two of his misses came on layups in the lane.
Cousins started slowly but had 15 points in the second quarter, and his 10 first-half rebounds gave him a double-double at the half.
The Nuggets led by 10 points midway through the first quarter but allowed the Pelicans to close the half on a 20-12 run. Denver was 10 of 19 from 3-point range in the first half, led by Harris with 18 points and 13 points each by Will Barton and Emmanuel Mudiay.
NOTES: New Orleans F Anthony Davis' left adductor strain has improved, but he missed his third consecutive game. Coach Alvin Gentry said he wants to see Davis do a little more in practice before he returns. ... Pelicans PG Rajon Rondo is averaging at least 11 points, 10 assists and six rebounds in December. "He's very good at finding open players," Gentry said. "He's very good at taking advantage of players' strengths. I think if you asked Jrue (Holiday) or anybody that plays with him, they'll tell you that he makes the game easier for them." ... The Nuggets were without C Nikola Jokic (left ankle) and F Paul Millsap (left wrist surgery). Coach Michael Malone said Millsap's hand is in a hard cast, but he expects him back working out with the team soon. "He's definitely getting better," he said. "We're hoping against hope that maybe by the end of this (six-game road) trip he can help out on the floor."