Nikola Jokic added 14 points and nine rebounds for Denver, which played without guard Gary Harris, who was excused for personal reasons. It was the first game Harris has missed this season. Barton started in his place.
Marc Gasol had 22 points and 11 rebounds for Memphis. Tyreke Evans and James Ennis III added 12 points each.
Trailing 54-50 midway through the third quarter, the Nuggets went on an 8-0 run, taking their first lead since the game's opening minutes on a driving layup by Jokic. Denver had a 67-60 advantage — its biggest lead to that point — heading into the fourth quarter.
Memphis pulled to within three, but the Nuggets scored 10 of the next 12 points, taking a 77-66 lead on Mason Plumlee's dunk off Malik Beasley's alley-oop pass with 6:15 remaining.
Memphis could not make significant inroads on Denver's lead the rest of the way.
Denver pulled within 47-43 at halftime after a lackluster first quarter in which Memphis went on a 15-0 run for a 23-8 lead before settling for a 10-point advantage at the close of the period.