With Denver leading 92-91, Arron Afflalo's 3-pointer jump-started the Nuggets on a 19-3 run to close out the game.
Anthony hit 14 of 21 shots from the floor and pulled down 11 rebounds. Nene had 10 points and 10 boards for the Nuggets, who were coming off a 1-3 trip and improved to an NBA-best 11-1 at home.
Anthony's three-point play put Denver on top 98-91 moments before Nene and Dwight Howard drew a double-technical for shoving each other under the Magic's basket. Anthony added a rim-rattler of a dunk that sent the satisfied fans streaming to the exits with two minutes left and his free throw with 1:34 left capped his night.
Howard had 21 points and 14 rebounds for Orlando.
Ty Lawson started at the point for Denver with Chauncey Billups out after aggravating his sprained right wrist at Toronto last week and he scored 16 points and dished out six assists.
Redick's point total was two more than his previous career high set Nov. 1, 2009, against Toronto.
One day after denying an ESPN report that he had told the Nuggets he'd only accept a trade to the New York Knicks, Anthony was greeted with cheers as he scored 20 first-half points.
But there were three young fans who loudly chanted "Let's trade `Melo!" and "You can go to New York!" while Anthony was at the free-throw line completing a three-point play in the first quarter. (They also chanted, "Put in Tebow!" later in the half).
Rumors about Anthony's destination have swirled since the summer when he was offered a three-year, $65 million extension that's collecting dust without his signature.
Anthony's three-point play was the highlight of a 12-3 run the Nuggets used to take a 61-51 lead in the closing seconds of the first half, but his baseline violation allowed the Magic to pull to 61-55 at the break when Marcin Gortat's put-back hung on the rim and then fell through the hoop as the buzzer sounded.
The Magic started the second half on a 9-0 run and the Nuggets didn't score until Sheldon Williams' jumper with 7:10 left in the third quarter.
With Denver leading 82-78 early in the fourth quarter, Redick sank a 3-pointer and was fouled by J.R. Smith, whose argument also drew a technical. Redick sank the technical free throw, then the bonus to complete a five-point trip.
Redick was 6 of 9 from beyond the arc.
NOTES: Nuggets coach George Karl was presented a golden ball trophy in pregame ceremonies to commemorate his 1,000th win last week in Toronto. ... Magic G/F Michael Pietrus sat out and will have an MRI on his sore left knee, Orlando coach Stan Van Gundy said. F Quentin Richardson (sore left elbow) didn't play. Karl said he doubts Billups will play Thursday night against San Antonio but is hopeful he'll be back against Minnesota on Saturday.