Playing without leading scorer Carmelo Anthony, the Knicks claimed the season series against their crosstown rivals.
New York announced prior to the game that Anthony would be shut down for the remaining two games after an MRI revealed a small tear in the labrum of his right shoulder. The injury will not require surgery and he will be reevaluated in a month.
Marcus Thornton netted 24 points for the Nets, who squandered an opportunity to lock up the fifth seed in the Eastern Conference.
Brooklyn now leads Washington by one game for the sixth seed in the East. The Nets close out their season on Wednesday in Cleveland, while the Wizards travel to Boston.
Washington owns the tiebreaker with a better head-to-head record.
Mason Plumlee tallied 16 points with nine rebounds and Paul Pierce dropped in 13 in the setback.
Pierce's 3-pointer to open the game marked his 1,000th point of the season, which made him the sixth player in history to record 1,000 points in 15 straight seasons.