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.
"I thought the effort was great and the defense was better," Nuggets coach George Karl said. "Arron offensively was really into the game and gave us a horse to ride a little bit."
Gallinari, who remains the team's leading scorer, was playing for just the third time since missing a month with a severely sprained left ankle. He missed his first six shots against the Hornets and finished with nine points on 3 of 10 shooting.
While Gallinari has been working his way back to his pre-injury form, Afflalo, who got off to a slow start offensively this season, has gone on a tear. He scored a career-high 32 points in last week's overtime win against Sacramento.
"I'm just starting to get locked in," Afflalo said. "I'm looking to play well for sure. When I play well, when anybody plays well, it's good for your mind. It's good for your team. It's good for the game and I want to allow it to help us win games."
Harrington said Afflalo's scoring surge was no surprise to his teammates.
"He had games like this last year so we knew he had it in him," Harrington said. "It's just him staying confident and when he gets his opportunities to capitalize on them."
Lance Thomas scored 18 points to lead the Hornets, who lost their fourth in a row.
"I didn't think as a whole we brought the energy that was necessary to get through those runs they made," New Orleans coach Monty Williams said. "They were playing in our paint. Obviously we have guys out there that don't know what we do, but some of the stuff that was happening it was just simple basketball plays and we weren't making them.
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 4 1/2 minutes of the final period.
After a pair of free throws by 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.
"They did what they pretty much always do in this building," Jack said. "They will manufacture runs at some point throughout the ballgame, for us it happened late in the third. It was kind of difficult for us to catch up from then on."
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 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.
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.