The crowd roared its approval during the opening introduction and for every basket and rebound from Anthony, who has yet to sign off on a three-year, $65 million extension that's been on the table since June, leading the Nuggets to explore trade options.
Sheldon Williams added 21 points and 14 rebounds for Denver (1-0).
Luke Babbitt led the Trail Blazers (1-2) with 18 points. Dante Cunningham had 15 points and 10 rebounds in Portland's second game in two nights.
Anthony converted two free throws to start the game, but Rudy Fernandez made his first three 3-point attempts and the Blazers led 26-24 after a quarter. Anthony watched the second quarter from the bench as Williams helped the Nuggets take a 57-49 lead into halftime with eight points in the period.
Anthony was back for the start of the second half, and his 3-pointer and two free throws by Nene extended Denver's lead to 64-49 early in the third quarter.
Babbitt hit a 3-pointer to get Portland within 78-65. Anthony's breakaway dunk and two more points got Denver's lead to 88-73 heading to the fourth.
Anthony's night was over when the Nuggets' lead increased to 100-79 on a 3-pointer by J.R. Smith in the first three minutes of the fourth quarter. Babbitt made his fourth 3-pointer of the game to make it a 103-89 game with 5:03 left before fouling out moments later.
The Nuggets were without Chris Anderson and Kenyon Martin. Both continue to recover from offseason surgery.