Anthony scored 22 points, including a layup with 56.5 seconds left, and the Nuggets blew a 26-point third quarter lead before recovering to beat the New Orleans Hornets 105-100 on Saturday night.
J.R. Smith scored 11 of his 17 points in the fourth quarter for Denver.
"Those last 4, 5 minutes it took a lot of courage to win that game," Nuggets coach George Karl said
It was the second straight game Anthony hit the deciding shot. Friday night, his 3-pointer with 0.1 seconds left beat Oklahoma City.
"Another day at the office," Anthony said. "We blew a lead tonight, but we won. I'll take that any day."
The Nuggets led 77-51 midway through the third quarter before New Orleans rallied. The Hornets outscored the Nuggets 20-6 to end the third, then scored the first nine points of the fourth to cut it 83-80 with 9:31 left.
"The team was fed up with the way it played in the first half," Hornets coach Byron Scott said. "We get to the point where we're not playing real well, things aren't going our way and we just buckle down."
Smith gave the Nuggets breathing room with a fast-break layup and a 3-pointer that made it 88-80 with 8:08 left, but Peja Stojakovic's fourth 3-pointer of the night tied it at 94 with 4:11 left. Chauncey Billups' two free throws gave the Nuggets a 96-94 lead, but Paul's 13-foot jumper with 2:42 left tied it at 97.
"Chris Paul did a great job coming down the stretch, but thankfully he didn't get it done tonight," Smith said.
Smith hit two free throws to give Denver a two-point lead, but James Posey hit a 3-pointer with 1:10 remaining to give the Hornets a 100-99 lead, their only advantage of the game. Anthony followed with a driving layup and, after a loose-ball foul on Paul, Billups hit two foul shots to give the Nuggets a 103-100 lead with 38.7 seconds left.
"I didn't want to shoot a jump shot," Anthony said of his finger roll. "I wanted to take it to the hole and either get fouled or make something happen."
Billups hit two more free throws with 22 seconds left to seal the win.
"We showed a lot of fight, but we lost," said Paul, who recorded his 24th double-double of the season. "There aren't any morale victories in this game."
Six players scored in double figures for the Nuggets, who have won five of their last six.
The Hornets played without center Tyson Chandler, suspended for one game for an altercation with Portland's Joel Pryzbilla on Friday night. Hilton Armstrong started in place of Chandler and had 17 points.
"We played fine," West said. "You have to play with what you have. Hilton played fine."
Billups scored five quick points to give Denver a 65-42 lead early in the third quarter, and Martin's layup gave the Nuggets their biggest lead at 77-51 with 5:52 left in the third.
The Nuggets, who were playing their fourth game and five nights, started a seven-game homestand after completing a four-game road trip. Karl said the homestand will give them a chance to get a stronghold on the Northwest Division title.
"It allows the opportunity to establish ourselves as contenders for the division," Karl said.
Hornets F Melvin Ely sat out with a sore right ankle. ... West has scored 20 or more points in four of his last five games. ... Both teams shot 50 percent from the field. ... The Nuggets are 22-9 since acquiring Billups from Detroit on Nov. 3.