Anthony scored 19 points after missing eight straight games because of an ankle injury, while Billups had 16 following a one-game absence, also due to an ankle problem.
“After sitting out two weeks, it’s kind of hard to come back and be yourself again,” Anthony told reporters.
“When the team’s playing so well, you don’t want to step in and overshadow anything. Just try to get everybody involved and let everybody continue building their confidence.”
In a dominating effort, the Northwest Division-leading Nuggets (35-17) posted seven players in double-figures for scoring.
Denver raced out to an 11-point lead after the first period and shot 61 percent.
Nene Hilario and Chris Andersen had 21 and 14 points respectively as the home team dominated and out-rebounded their opponents 47-28.
The defeat was the slumping Southwest Division-leading Mavericks (32-20) worst of the season, Dirk Nowitzki managing a team-high 17 points in their fifth loss in seven games.
Jason Terry tallied 16 while Josh Howard put up 14 for Dallas, who could not repeat their Dec. 27 victory in Denver.
The Nuggets defeated the Mavericks 4-1 in last season’s best-of-seven Western Conference semifinals and both teams are jockeying for positioning again this year.
“Coming out of the break every game is critical,” Terry said. “If you look at the Western Conference, the race is nip and tuck.”