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"It was one of them shots, that you know is going to go in," said Anthony, who finished with 31 points on 12 of 24 from the field. "I had plenty of shots this whole game like that, and they didn't go in. That particular one felt real good."
The play was set up for a pick-and-roll with Amare Stoudemire on the left side of the lane. But the Grizzlies overplayed Stoudemire, leaving Allen 1-on-1 with Anthony.
"He had been guarding me close up the whole night," Anthony said. "I just wanted to get a little bit of space, just something where I could see the basket. Once I made a jab move, I got a little bit of space."
Memphis had one more chance, but an alley-oop attempt to Darrell Arthur was broken up at the basket, giving the Knicks their third straight win and strengthening their hold on the sixth playoff spot in the Eastern Conference.
"It was just trying to get a lob, and they played it," Memphis coach Lionel Hollins said. "We could have tried to get a shot, but they were going to switch all that, so I thought we'd just try to get a lob.
"It's a play we have run before. It just didn't work."
Stoudemire added 26 points for the Knicks, while Toney Douglas finished with 18 points and a career-high 10 assists.
The Knicks won despite 17 turnovers and Memphis' 33-4 advantage at the free throw line. However, New York connected on 12 of 24 outside the arc. The Knicks are now 13-1 when they hit at least a dozen 3-pointers.
"It was a tough game," Randolph said. "We didn't come out from the start very disciplined. We didn't guard the 3-point shot. They hit a lot of shots, and our defense wasn't good. That's the game."
Memphis' final rally came on 10 unanswered points, capped by Randolph's three-point play with 14 seconds left, before Anthony's jumper from the wing.
"We had a chance to put them away," Stoudemire said, "but the Grizzlies came on strong. They really got it going."
New York led by as many as 17 in the third quarter while shooting nearly 60 percent, but its 6-of-20 shooting and careless ballhandling in the fourth period allowed Memphis to catch up.
"We had to hold them off. They're good," New York coach Mike D'Antoni said. "They got into us, and, obviously when they shoot 35 foul shots, and we shoot four, we had to make it up elsewhere. We just shot the ball extremely well."
The track meet was on early with New York making 10 of its first 11, including all four from outside the arc.
The Grizzlies stayed in it with their defense that leads the league in forced turnovers and steals. Memphis caused 10 Knicks' miscues in the first half, nine of them on steals.
Despite that and a 14-1 advantage at the free throw line, the Grizzlies still trailed 61-53 at the break as Anthony had 20 points and Stoudemire 16.
New York took control at the opening of the second half. The Knicks were perfect on their first four shots and pushed the lead to 74-57 before carrying a 96-82 advantage to the fourth.
Arthur opened the final frame with eight straight points, cutting the Knicks' lead to 96-90. But a 3-pointer by Shawne Williams stopped the Memphis rally, and Anthony's inside bucket built the advantage back to double digits.
D'Antoni said he didn't call timeout before the winning play, and left it up to Stoudemire and Anthony to work through it. He thought the Knicks' advantage was to play through Randolph's three-point play and not let the Grizzlies set up or make defensive substitutions.
"That's too much stuff," D'Antoni said. "We've got guys that know how to play, and when we call timeout to put the ball in Melo's hands, it's like 'Duh.'
"That's where it's going to go. We knew it, and we got it done."
- The Knicks are 6-3 since the trade that brought Anthony and Chauncey Billups to New York. Billups missed his fifth straight game with a left quad injury. "I think he's feeling a lot better. He's not quite ready yet," D'Antoni said in his pregame availability. "Just a little bit of pain. We just want to be very cautious." As for whether he would be ready for Thursday's game at Dallas, D'Antoni replied: "You don't even know when it's going to be. When he's ready, he's ready."
- The Knicks did have Ronny Turiaf and Bill Walker available after missing several games each with injuries.
- Memphis G Jason Williams sat out with lower back stiffness.
- The Grizzlies said F Rudy Gay, who has missed nine straight games with a shoulder injury, will have an MRI on Monday to see about the healing progress.