Chauncey Billups added 18 points and Al Harrington contributed 14 points and eight rebounds for Denver.
Jason Terry scored 26 points and Dirk Nowitzki had 23 for the Mavericks, who have lost two of their first three home games.
The teams met in Denver on Wednesday night, with Dallas pulling out a 102-101 victory behind Nowitzki's 35 points. This time, the Nuggets pulled away in the fourth quarter after it was tied at 79 after three.
Anthony hit three 3-pointers in the final 3:47 and scored 15 points in the third, but was on the bench for most of the Nuggets' 12-4 spurt to start the fourth. The run started and ended with dunks by Harrington, giving Denver a 91-83 lead with 7:23 left, and the Mavericks never recovered.
Terry had one point and Nowitzki went scoreless in the fourth quarter.
Denver clung to a 53-52 advantage at the break behind 6-for-9 3-point shooting. Terry's 23 points were among the few Dallas highlights, with Terry draining a 3-pointer with 5.9 left until halftime to get the Mavericks close.
The Nuggets went with a small lineup including 6-foot-9 Sheldon Williams as the tallest starter, and Denver assumed a 26-24 lead after one quarter as Dallas committed six turnovers in the first 12 minutes, 10 in the first half.
Late in the second quarter, Anthony got into a playful exchange with some heckling fans. Anthony was laughing during the give-and-take.
Denver was coming off Friday night's 111-104 home victory over the Clippers. The Mavericks had been idle since Wednesday night.
Notes: Denver C Nene missed his third straight game with a strained left groin. Fs Kenyon Martin and Chris Anderson are out indefinitely while recovering from knee surgeries. ... Dallas began a stretch of 15 home games over a 22-game span.