The Knicks had a 14-point lead in the third quarter only to see the Magic storm back behind the stellar play of Oladipo, who had two huge three-point plays in the second overtime to seal New York's fate. He finished one rebound shy of a triple-double.
Arron Afflalo poured in 32 points, but he turned his ankle midway through the second extra session and had to leave the game.
Anthony was sensational for the Knicks, once making nine straight field goals. He shot 16-of-28 from the floor overall and made six of his 10 three-point attempts. He also grabbed 11 boards.
It wasn't enough, though, as shoddy defense and tired legs ended up dealing New York's playoff hopes a critical blow.
The Knicks were outstanding from beyond the arc, going 15-of-34 as a team, but they were outscored 54-28 in the paint.
Orlando shot 49.7 percent overall and went 22-of-26 from the free-throw line.
Nikola Vucevic, who fouled out in the second overtime, chipped in 14 points and 15 rebounds for the Magic.
New York, which now sits four games back in the loss column of a playoff spot, has now lost seven of its last nine games.