Anthony's much-hyped matchup with James will have to wait until Feb. 18 because of a nagging knee injury that kept him out of his fourth straight game.
The Nuggets didn't need 'Melo to send James to his sixth loss in seven trips to the Pepsi Center.
Kenyon Martin filled in nicely for Anthony, scoring 19 points, grabbing 12 boards and playing tough defense on James down the stretch, forcing him to miss a layup and then inducing him to step out of bounds on back-to-back possessions in the final minute.
"Those were big stops," teammate Anthony Carter said. "K-Mart won the challenge."
If only begrudging respect from King James.
"I think Kenyon is really good laterally, he's a physical guy," James said. "As far as problems, I don't think he presents any problems. But he definitely did a good job of standing in front of me the last couple of possessions."
Nuggets coach George Karl said he made the right call by not putting Martin on James too early. He stuck with Aaron Afflalo and Joey Graham until the final minute.
"I was just trying to make it tough on him," Martin said. "He's a great player and of course, the ball was going to be in his hands. I just was going to make him take a tough shot. I'm always doing my job on that end. He's a great offensive player, a great player, period."
And Martin is a great defender, Chauncey Billups insisted.
"He doesn't get enough credit, but he always takes the toughest matchup every night," Billups said.
The Nuggets went on a 10-1 run to turn an 89-86 deficit into a seemingly safe 96-91 lead.
Despite committing eight turnovers and missing 16 shots, James scored 35 points and wouldn't go down easily. He sank a 3-pointer with 11.8 seconds left that made it 96-94.
J.R. Smith's two free throws with 11 seconds remaining gave Denver a 98-94 lead, and James misfired a 3-pointer at the other end. But when Nene missed two free throws for Denver, James made a 3-pointer with 1.2 seconds left to pull Cleveland to 98-97.
Following a timeout, Billups, who returned to the Nuggets lineup after missing eight of Denver's previous nine games with a strained left groin, took Martin's inbounds pass and was fouled by Delonte West.
He sank his first free throw with 0.2 seconds left and missed the second one intentionally, then celebrated the Nuggets' biggest win so far.
"They were missing an All-Star of course in 'Melo, but they were able to get another one back in Chauncey," James said.
Nene returned from a sprained ankle and scored 20 points to go with Billups' 23.
ESPN was on hand for what the network surely hoped would be a LeBron-'Melo matchup, but Anthony wouldn't be swayed.
"It would be the same if I was playing Minnesota. My health is more important right now," Anthony said after missing the Nuggets' shootaround. "Maybe five or six years ago, if somebody told me I had a chance to play against LeBron, I probably would go out here and be stupid and play on an injured leg and not even care about that.
"I've got to be smarter than that. I want to play in this game more than anybody out there, but unfortunately, I (can't)."
Denver trailed 91-88 with 90 seconds left.
"We gave ourselves an opportunity to win, but one thing we can't do is turn the ball over a lot like we did, including myself," James said. "Me, personally having eight turnovers, probably five or six of them unforced. We can't do that on the road."
Despite Cleveland's 19 turnovers and 62 percent foul shooting, along with a tough goaltending call whistled on him in the fourth quarter, James said he wasn't frustrated.
"We're playing too good of basketball to be frustrated with one game," he said. "Happy that we gave ourselves a chance to win. Down the stretch, being up three, those are the times we usually get a stop and then make a backbreaking play. Give a lot of credit to Denver. I feel like we played well enough to win, but we shot 60 percent from the free throw line, we turned the ball over 20 times. That can't help us."
Neither could Anthony's absence.
Ty Lawson (ankle) remained sidelined for Denver. ... James is 4-9 against the Nuggets. ... Denver's Chris Andersen (ankle) also returned to action. ... K-Mart has 15 games with 10 or more boards after collecting just seven double-digit rebound performances in 66 games last season.