Raymond Felton added 15 points and J.R. Smith and Pablo Prigioni had 11 for New York, which shot a season-high 57.3 percent from the field.
The Knicks took advantage of Davis' absence as Chandler and Stoudemire had a free run on the inside. New York dominated in the paint, outscoring Orlando 54-42, on a night that Anthony broke Richie Guerin's team mark.
"Any record that you have a chance to get or break or tie, that is the fun part," said Anthony, who was 8 of 17 from the field. "Tonight was my chance to break the record. It makes it fun out there when you are looking forward to something. Records are made to be broken."
Guerin, who is 80 and retired in Florida, congratulated Anthony on the MSG Network's postgame show.
"...in today's day and age, with three point shot, a lot of records are meant to be broken. It couldn't happen to a better guy," Guerin said.
The Knicks big run came in the third quarter right after Redick hit a 3-pointer to tie the game at 62 with 7:20 to go.
Chandler, who had been in double figures only once in his last seven games, tipped in a rebound and scored on an alley-oop from Smith and Stoudemire tallied on a driving layup for a 68-62 lead.
The Magic twice cut the deficit to four points, but Stoudemire slammed home a dunk and Prigioni nailed a 3-pointer to stretch the lead to 75-68 and Orlando never threatened again.
Nelson and Redick kept the Magic in the game in the first half, combining for 36 points on 14 of 20 shooting from the field. Redick made his first seven shots, including three from long range, and didn't miss until late in the half.
NOTES: Guerin had the Knicks old record of 29 straight 20-point games, set in 1961-62. ...This is the second game on a four-game road trip for Orlando, which has games left at Boston and Milwaukee. ...New York is 16-6 at home this season. ...The Knicks played without backup point guard Jason Kidd, who was out with a sore lower back. ...Afflalo, who was averaging 16.7 points, missed his second straight with a strained left calf.