Anderson made seven 3-pointers and scored 31 points, and the New Orleans Pelicans overcame Davis' loss to a broken left hand to hand the Knicks their ninth straight loss, 103-99 on Sunday night.
"When Ryan comes into the game, he doesn't think like a bench guy," Pelicans coach Monty Williams said. "He thinks like `I'm playing 35 minutes and I've got to do my job'. Obviously we don't expect him to score 31 points, but I will take it."
Tyreke Evans added 24 points, including 10 in the fourth quarter, as the Pelicans sent the Knicks to their seventh straight home loss.
"Obviously we played against a desperate team tonight," Williams said. "But, we're desperate, too. Any time you can win on the road, winning eight games period, is special in the NBA."
The Pelicans, now 8-8, are last in the NBA's Southwest Division but would be in first place in the Atlantic. Toronto currently is atop the standings at 6-10 - and the last-place Knicks (3-13) are only three games back.
Davis had seven points and four rebounds in the first quarter before leaving with what the Pelicans said was a non-displaced fracture in his left hand. The team said a timetable for his return has not been determined.
"I was going up for a lob, got fouled and then hit my hand on the rim," Davis said. "I haven't found anything out yet. Most definitely I hope it's a short-term thing. I didn't think it would keep me out, but it did."
Carmelo Anthony finished with 23 points and 10 rebounds, while rookie Tim Hardaway Jr. had a career-high 21 points for the Knicks, who haven't won at home since beating Milwaukee on Oct. 30 in their season opener.
"Nine straight, eight straight, whatever we lost, we just can't seem to get it together," Anthony said. "Can't seem to figure it out, but we have to. We don't have no choice but to figure this out."
In a game that featured 12 ties and 17 lead changes, the Pelicans trailed 93-88 after Hardaway's 3-pointer with 6:42 remaining. However, New Orleans then scored the next 10 points, as Evans started the streak with a three-point play and ended it with two free throws with 2:46 left.
The Knicks pulled within three on Anthony's 3-pointer with 54 seconds left. But, after a Pelicans turnover, Hardaway and Anthony missed potential game-tying 3s and Evans hit a free throw with 15 seconds remaining to secure the win.
"I thought down the stretch we played on our heels," Knicks coach Mike Woodson said. "We had so many breakdowns again on the ball defense. We are not taking pride in guarding. I've got to find some identity with this team. Somehow we have to get this monkey off our back."
Neither team led by more than seven points in the game.
A 19-8 run by the Knicks gave them their biggest lead of the game, 49-42, on Hardaway's 3-pointer with 19 seconds left in the second quarter. Anderson scored inside with a second left before halftime to make it a five-point game.
"We knew we had to step up defensively and eliminate easy shots and we did that in the second half," said Anderson, who also made seven 3-pointers in a game at Madison Square Garden while playing for Orlando during the 2011-12 season. "We outplayed them and imposed our will."
New Orleans had an 8-0 run in the third to open its biggest lead at 76-69 on Evans' layup with 52 seconds left.
"We lost and it's killing me right now," Felton said. "We need to find a way to end this losing streak. I don't care how ugly it is."
The win for the Pelicans was just their second in the last 10 meetings between the teams.
NOTES: The last time the Knicks lost nine in a row was March 19-April 4, 2006, under Larry Brown. The Knicks also lost 10 in a row that season from Jan. 28-Feb. 13. The Knicks haven't won since a 95-91 victory at Atlanta on Nov. 13.