Anthony poured in 30 points and Billups had a magnificent clincher with 28 points, seven rebounds and 12 assists, as the Nuggets beat Dallas, 124-110, disposing of the Mavericks in five games in their conference semifinal series.
Denver was denied a sweep on Monday in a 119-117 loss at Dallas, but two nights later the Nuggets dominated in an up-tempo style and led nearly the entire game.
J.R. Smith scored 18, Nene 17 and Kenyon Martin 15 for the Nuggets, who will play either the Los Angeles Lakers or Houston Rockets in the conference finals. The Lakers hold a 3-2 lead in the other conference semifinal series and can advance with a victory Thursday in Houston.
The last time Denver made it this far it lost in five games to the Lakers in the conference finals. LA won the championship that season, beating Boston.
"It just seems like everybody wants to talk about when we're going to crack, when we're going to falter," said Nuggets coach George Karl. "I'm sure they'll say the same thing the next series. I don't have that worry. We're not totally grown up, we're not totally an experienced-enough team. There's a smart toughness to our team."
Denver also won its 16th consecutive home game. The Nuggets haven't lost at the Pepsi Center since March 9 against Houston.
"I don't know if the Denver fans have ever been known as the sixth man, but it's a pretty special building," said Karl. "To see everybody stay after the game was a nice feeling. It doesn't happen very often in the NBA where most of the people were there still cheering five, 10 minutes after the game."
Billups is in a familiar position, in the conference finals for a seventh straight year. His first six were in Detroit, where he led the Pistons to the NBA title in 2004. He was traded to Denver early this season in the deal that sent Allen Iverson to the Pistons.
"It's absolutely been a storybook season," said Billups. "I couldn't write a better script for me coming home, trying to lead the team I always grew up watching and rooting for. It's unbelievable. Hopefully I don't wake up anytime soon."
Dirk Nowitzki scored 32, pulled down 10 rebounds and had seven assists for Dallas, which shot 12-of-34 from three-point range in the concluding game of the physical series that also had its off-court issues with Mavericks owner Mark Cuban yelling at Martin's mother after Denver's controversial Game 3 win.
The Nuggets shot 63.8 percent in the first half, led by Anthony's 21 points on a 9-of-11 effort and Denver carried a 69-55 lead into the second half.
Jason Kidd started heating up for the Mavs, drilling a trio of three-pointers in the third quarter, but Dallas couldn't keep up with the quicker Nuggets.
Smith banged in a three-pointer later in the period, providing a 93-76 lead with under three minutes remaining in the stanza and the margin stood at 94-80 moving to the fourth.
Nowitzki's layup had Dallas within 103-97 with nearly seven minutes remaining, but Anthony then drilled the biggest shot of the game, a three-pointer with the shot clock about to expire.
"It was a lucky shot," said Anthony. "That sparked our momentum, though. After that shot we got out in transition, got some easy baskets, got some stops."
Dallas' Antoine Wright was then called for a technical foul for pushing Smith in retaliation for being elbowed. The Mavs were never closer than seven after that juncture.
"These guys are a legitimate championship-caliber team," said Mavericks coach Rick Carlisle. "They've got a great shot, they've got a real opportunity. It'll be interesting to watch how it all comes down."
Carlisle chose to insert Terry in the starting lineup and his three-pointer gave Dallas a 10-4 lead, but Denver went on an ensuing 18-4 run and didn't trail again. Nene's jam off some nifty passing capped the spurt.
Denver was ahead 34-27 after one quarter, and Billups played a big role in the second, sending a touch pass to Nene for a jam in transition and a 57-43 cushion inside five minutes left.
Game Notes: Carlisle arrived at Pepsi Center about an hour before tip-off. He was in South Florida to serve as a pallbearer at the funeral of Hall of Fame coach Chuck Daly...Kidd scored 19, Brandon Bass 17, Howard 14 and Terry 11...The Nuggets shot 58.5 percent to 51.4 for Dallas.