Afflalo had a season-high 19 points and hit two 3-pointers in overtime to help the Denver Nuggets beat the Hornets 116-110.
Chauncey Billups had 20 points and nine assists as all five Denver starters scored in double figures.
The loss comes after the Hornets won two straight games on buzzer-beating layups by James Posey. Saturday, the hero was Afflalo, who rebounded from a poor outing against the Hornets on Dec. 18. Afflalo was 2 for 9 and missed all six of his 3-pointers in that 98-92 loss.
"It's nothing I took into this game," Afflalo said. "It was a brand-new opportunity."
He made a career-high five 3-pointers.
"Arron hit some huge shots tonight," Billups said. "I just told him just stay focused, you're the one who's going to get the looks. They're not going to sink off me and give me a look, and Melo, you saw how they played him."
With the Hornets focusing their defense on Anthony, Afflalo stepped up. His first 3-pointer of overtime gave Denver a 106-101 lead, and after Paul hit his only 3 to make it 108-106, Afflalo struck again with 1:33 left.
"There's always a weakness to the double team and I thought Melo did a good job of getting us a good shot," Nuggets coach George Karl said. "In overtime Afflalo's two 3s were huge. We're not a pretty team, we just win games."
The Nuggets didn't escape the game unscathed. Anthony rolled his left ankle after landing on Devin Brown's foot with 1:04 left, but stayed in the game and hit two free throws to give Denver a 113-106 lead.
"It's better than I thought," Anthony said. "It looked pretty bad at first, but it's better than I thought. We'll see how it is [Sunday]."
The Nuggets had a chance to win the game before overtime. They led 101-99 with 24 seconds left, but Paul hit a shot to tie it with 18 seconds left.
"We had our chances in regulation," Hornets coach Jeff Bower said. "It was going to be hard for us to win the game in overtime."
Anthony missed two shots in the final seconds that would have won it in regulation.
"I thought we had it won when Melo got the tip-back but he just missed it," Billups said. "In the overtime we were focused and took the game over."
It was a struggle for Denver until then. Stojakovic hit three 3-pointers in the third quarter as New Orleans surged ahead, but the Nuggets came storming back. Anthony hit a turnaround and after New Orleans miss, Martin's putback dunk made it 75-72 with 2:59 left in the frame.
Denver led 79-78 heading into the fourth.
"The attention of our team, our effort and our concentration is outstanding," Bower said. "I thought we played every possession and tried to do what we wanted to do on every possession. It didn't always work, but we gave ourselves a chance to win."
West, the Hornets' second-leading scorer, missed the game after spraining an ankle against Minnesota on Friday night. Songaila started in West's place and scored eight points in the first quarter to help New Orleans take a 33-32 lead.
"In basketball, when a guy is out, different guys step up," Paul said. "Darius was real big tonight."
The Nuggets had four players with more than 10 rebounds and held a 61-37 edge on the boards. ... Martin has 15 double-doubles this season. ... Stojakovic has hit at least three 3-pointers in 14 games this season.