The Magic trailed 58-47 at halftime, but surged in the second half as the Knicks struggled from the field.
The win was the Magic's third straight and fifth in six games. It was also Orlando's second win this season over the Knicks, who host the Magic twice before the end of the month.
Amare Stoudemire and Billups led New York with 30 points apiece, followed by Anthony with 25.
The Knicks led 84-79 entering the final period before an 8-2 Magic spurt, capped by a basket by Quentin Richardson, closed them to within 88-87 with 9:27 to play.
Orlando took a 90-88 lead on its next possession on Ryan Anderson's 3-pointer.
Billups was fouled on a 3-point attempt with 7:31 left and hit all three free throws to briefly put the Knicks back up 93-92.
But the Magic quickly responded with five points, including a 3-pointer by Jason Richardson, to regain a 97-93 edge with 6:48 remaining.
Stoudemire completed a three-point play to close the gap to 99-96, before Nelson reeled off nine straight Magic points to put the them up 108-99 with 4:35 left.
The Knicks got within four points at 110-106 on a pair of free throws by Billups, but did not get any closer.
In a physical first half, in which 26 fouls were called, the Knicks were the much crisper team on the offensive end as they built a 58-47 lead.
The action was fast-paced throughout and featured nine lead changes.
Orlando trailed 15-14 with just under five minutes left in the first quarter before going on a 12-0 run to go up 26-15 with 2:47 left in the period. The Magic took a 32-21 lead into the second quarter.
The Knicks responded with 21-7 run to start the second to take a 42-39 lead at the 5:56 mark and stayed on top the rest of the half.
They got some help with 4:01 remaining, when Magic forward Hedo Turkoglu was ejected after picking up his second technical foul of the game. Turkoglu was on the bench with three personal fouls and apparently said something to referee Jason Phillips.
Turkoglu played only 12 minutes, going 0 for 4 from the field, with two rebounds and two assists.
Howard led all scorers in the first half with 22 points on 7-of-10 shooting. But the rest of his teammates were just a combined 7 for 21. They also turned the ball over 11 times, leading to 10 New York points.
The Knicks only shot 40 percent, but got 16 points from Billups, and 15 and 11 from Stoudemire and Anthony, respectively.
Notes: Billups left after a collision with Howard with 2:13 left in the game and didn't return. ... Magic G Gilbert Arenas was inactive Tuesday night with a sore left knee. ... With his ninth rebound in the third quarter, at 25 years and 83 days old, Howard became the youngest player in NBA history to amass 7,000 rebounds during his career. He passed Wilt Chamberlain, who was 26 years and 128 days old. ... New York Yankees pitcher Joba Chamberlain was in attendance Tuesday.