Kenyon Martin added 18 points and Nene had 16 to round out a balanced attack by the Nuggets (8-4), who have won four straight and seven of eight overall since Billups joined the lineup following a blockbuster trade that sent Allen Iverson to Detroit.
"Denver has got a good club that can compete with anybody," Spurs coach Gregg Popovich said. "Chauncey is a great addition."
The Nuggets also played strong defense, holding Tim Duncan to 12 points while snapping San Antonio's three-game winning streak.
Denver has looked to bolster its defense since training camp. Billups, who arrived five games into the season, thinks he fits in with that approach.
"They said everything they did before I came was all about defense," Billups said. "I think me coming, and coming with a defensive mind-set, it just enhances that."
Still playing without All-Star guards Tony Parker and Manu Ginobili, the Spurs (5-6) failed to move above .500 for the first time this season. They shot 39 percent from the floor and were led by rookie George Hill's 20 points. Michael Finley had 13.
Parker and Ginobili, both sidelined by ankle injuries, are expected back sometime in December.
With Duncan having trouble inside, San Antonio had no answer from on the perimeter. The Spurs went 2-of-17 from 3-point range.
Duncan was 4-of-13 from the field and fell way short of his season average of 23.9 points.
"I don't let Tim do what he wants to do. Never have and never will," Martin said. "You try to make it tough as possible on him, not give him the easy looks that he wants."
After missing a turnaround bank shot from about 10 feet with Martin guarding him, Duncan groused about it down the floor and was called for a technical foul with 1:25 remaining in the third quarter.
Anthony made the free throw, which was followed 10 seconds later by a defensive 3-second call against the Spurs and another successful foul shot by Anthony.
The Nuggets kept possession, and in another 8 seconds Billups made a 3-pointer to give Denver a 73-53 lead.
"We had a couple of situations where we were just on the verge of something, and then something goes wrong," Spurs forward Bruce Bowen said.
Billups, last week's Western Conference player of the week, went 5-of-8 from the floor and added a 9-for-9 performance from the free-throw line in 40 minutes.
"We've had a tough eight or nine games where we've played some tough teams in some tough buildings, and we've been successful," Billups said. "We've just got to try and continue to build on what we've done."
Denver led 21-20 after the first quarter. Even though the Spurs made two of their first three shots to open the second, the Nuggets led 31-23 because they were more active around the basket.
It got worse for the Spurs. They missed their next nine shots and didn't score for 3 minutes, falling behind 36-27 with 5:57 left in the first half.
San Antonio missed three more in a row -- all of them layups by Duncan or Hill -- and fell behind 44-33 with 3:14 left before halftime.
Denver took a 10-point lead at halftime after Martin shot 5-of-8 from the floor in the second quarter compared to 0-for-3 for Duncan.
"Denver played well enough to beat us," Popovich said. "They played aggressively."
Nene, the NBA leader in field-goal percentage at .650 coming into the game, was 5-of-5 before he missed his first shot in the second half.
Popovich said Parker and Ginobili are progressing quicker than expected, particularly Parker. "He did a good job elevating the leg and getting on his crutches so the swelling would get out of there pretty quickly," Popovich said. ... It was Denver's seventh victory in the last 37 tries at San Antonio. ... Popovich called a timeout 33 seconds into the game after the Nuggets scored on a slam dunk by Martin off a long pass from Anthony. The Nuggets tried it again about a minute and a half later, but Hill was back and got in front of Billups' pass for the steal. ... Spurs reserve Blake Ahearn was signed during the team's West Coast road trip this week and all the club had for him to wear was No. 18. He switched to jersey No. 19 when San Antonio returned home Wednesday.
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