Walker added six assists and five rebounds for Charlotte, which logged an away win for the first time in 16 games stretching back to last season.
His jumper over the Knicks' Carmelo Anthony with 55 seconds left in the game secured the victory.
Gerald Henderson contributed 18 points and Michael Kidd-Gilchrist helped out with 16 as the Bobcats improved to 2-2 on the season.
Anthony poured in 32 points and Metta World Peace came off the bench for 18 as New York dropped a third straight.
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