Kidd's trey was his second in the final frame for the Knicks, who erased a six-point deficit down the stretch and evened the season's series between the New York rivals at one win apiece.
The former Net finished with six 3-pointers overall en route 18 points, six assists and six rebounds, while Anthony connected on 15-of-24 shots from the field, including 5-of-7 from 3-point range.
The win was the sixth in seven contests for the Knicks.
Brooklyn, meanwhile, fell for the fifth straight game despite 18 points and 10 assists from Deron Williams.
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