Chauncey Billups made a triumphant return to the Nuggets with 15 points, Anthony scored 28 and Denver beat the Dallas Mavericks 108-105 on Friday night.
Billups also had three assists and three steals, including two down the stretch.
Jason Kidd finished with 22 points, 10 rebounds and nine assists for the Mavericks.
Anthony hit four big free throws in the final 12 seconds. After Jason Terry's 3-pointer cut Denver's lead to 106-105, Anthony made two foul shots with 0.4 seconds remaining to seal the win.
Gerald Green's shot at the buzzer bounced off the rim. Kidd had a chance to tie it at 103 with 21.6 left, but missed a free throw.
Nene had 19 points and reserve J.R. Smith scored 15 for the Nuggets, who led by as many as 10 in the fourth quarter.
Green scored all 13 of his points in the final period, Dirk Nowitzki finished with 23 points and 10 rebounds, and Brandon Bass had 12 points and 10 boards.
Billups, Antonio McDyess and Cheikh Samb were acquired from Detroit on Monday in exchange for Allen Iverson.
However, McDyess' days in Denver are done.
His agent, Andy Miller, said the two sides have reached an agreement in which the forward will be bought out of his contract.
Miller didn't want to speculate about McDyess' future, saying they needed to get over this hurdle first.
"We're just real appreciative of (the Nuggets') flexibility," said Miller, who was on hand to watch Billups' homecoming.
Samb suited up but didn't get into the game.
Since his first stint with the Nuggets from 1998-2000, Billups has blossomed into a pure guard, the floor general coach George Karl has been craving since the team dealt away Andre Miller to acquire Iverson nearly two years ago.
Billups played more than 30 minutes against Dallas and struggled with his shot, going 5-for-17 from the floor.