Johnson's baseline jump shot broke an 84-84 tie and Deron Williams added three foul shots in the closing seconds to secure the victory for the second-place Nets, who cut the Knicks' lead atop the Atlantic Division to one game.
Williams finished with 14 points, 12 assists and five rebounds while Brook Lopez contributed 14 points and 11 boards as Brooklyn reeled off its ninth triumph in 10 contests.
Kris Humphries provided a double-double of 11 points and 13 rebounds.
Carmelo Anthony pumped in 29 points and dished off seven assists for the Knicks, who lost for the fourth time in six outings.
J.R. Smith scored 16 points but missed a potential score-tying 3-pointer at the buzzer for New York.