Anthony's trey with 8.2 seconds remaining in the extra frame gave him a season-high 43 points for the game and handed playoff-hopeful New York a key victory.
They entered the contest one game ahead of Milwaukee for the eighth and final Eastern Conference postseason berth.
The Knicks, who once led by 21 points, forced overtime after rallying from a 10-point, fourth-quarter deficit. Anthony tied it up with 11.2 seconds left on another 3-pointer.
He finished the game 16-of-31 from the field.
New York spoiled the return of point guard Derrick Rose to the Bulls' lineup. The reigning NBA MVP had missed 12 games with strained groin.
Rose scored 29 points but failed to pull out a last-second, overtime win when his shot from the left baseline bounced off the rim at the final buzzer.