Carmelo Anthony, who spent the first 7 1/2 years of his career in Denver, received a warm reception from the crowd during pregame introductions. He had 20 points for Portland, and CJ McCollum added 15.
Trailing by seven at halftime, Portland cut the deficit to one on Damian Lillard's 3-pointer late in the third quarter. But the Nuggets scored 10 straight points in the last 2:33 of the period, including two 3s by Grant, to rebuild their lead to 89-78 going into the fourth.
Barton's 3-pointer with 9:43 remaining put the Nuggets up 96-80, their biggest lead to that point, and Denver maintained a double-digit advantage the rest of the way.
The finish was a departure from recent meetings. The previous seven regular-season encounters between the Nuggets and Trail Blazers had all been decided by single digits.
Denver, which lost to Portland in the Western Conference semifinals last season, has won the first two matchups this season, including an opening-night victory at Portland that snapped its 18-game winning streak in home openers.
Harris hit three 3-pointers in the first half, helping the Nuggets take a 62-53 lead.
Trail Blazers: C Jusuf Nurkic, working his way back from a broken lower left leg suffered last March, ran the stands at the Pepsi Center during the team's shootaround. Nurkic has been doing conditioning and shooting drills in recent weeks. The team hasn't given a timeline for his return, but coach Terry Stotts said before the game, "He is doing everything he is supposed to do behind the scenes."
Nuggets: Jamal Murray was back on the floor after leaving Tuesday night's game at Philadelphia in the opening minutes with what the team described as a "trunk contusion" following an on-court collision. Murray finished with 12 points.
Trail Blazers: Visit the Phoenix Suns on Monday night.
Nuggets: Continue a five-game homestand against Oklahoma City on Saturday night.