The Wizards won for just the eighth time all season and halted their most recent losing streak at six.
A three-pointer by James brought Washington within a point with 2:01 remaining and Nick Young put the Wizards in front for good with a jumper 19 seconds later.
James made another long-range shot with 1:06 to play, giving Washington a 91-87 cushion.
The Knicks missed nine shots and turned the ball over twice while the Wizards were staging their comeback. New York had won its previous two games.
Antawn Jamison led Washington with 28 points and James had 19.
Al Harrington had 18 for New York.
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