Nene added 12 points and Ty Lawson had 11 points to go with 10 assists for the Nuggets, who have won five of six since the All-Star break.
Lance Thomas scored 18 points to lead the Hornets, who lost their fourth in a row.
Jarret Jack added 17 points and Xavier Henry and Marco Belinelli had 12 points apiece for New Orleans.
Locked in a tight game most of the way, the Nuggets used a 10-2 run to pull out to their biggest lead to that point, 74-63 with 2:58 left in the third period.
Harrington scored five points in the run, including driving the lane for a dunk and Afflalo finished it off with a 3-pointer.
Chris Kaman responded with successive baskets and the Hornets fought back to within 79-71 going into the fourth quarter.
But the Nuggets again asserted themselves, outscoring the Hornets 16-6 over the first 4½ minutes of the final period. After a pair of free throws by Lance Thomas pulled New Orleans within six points, Harrington hit a 3-pointer and Andre Miller soon followed with a driving layup as part of the run putting Denver in command 95-78 with 7:25 left to play.
New Orleans got back within 97-85 after Jack made a 3-pointer and Henry had a layup but the Nuggets put the game away by scoring seven points, with Chris Andersen and Danilo Gallinari each muscling in dunks to help push Denver's lead back to 17 points.
Afflalo scored 13 of his points in the first half when Denver took a 50-46 lead over the Hornets.
The Nuggets shot 72.3 percent from the floor en route to a 32-26 first-period lead with Afflalo hitting all four shots he took from the field.
NOTES: Forward Jeff Foote was signed to a 10-day contract by New Orleans prior to the game. A 7-footer who can also play center, Foote bolsters the Hornets' front-court depth. ... The Nuggets were without center Timofey Mozgov for a second consecutive game because of a left ankle injury.