The Wizards remained winless in seven games this season, their worst start in franchise history, and are the only team in the NBA without a victory.
They appeared ready to break through when they built a 15-point lead in the second period, but New York cut its deficit to a single point at intermission and the Knicks led for much of the second half.
Wall then missed a 3-point try with 10 seconds remaining and New York's Iman Shumpert hit 1-of-2 foul shots with 5 seconds left.
After a timeout, Washington's Nick Young failed on a 3-point attempt that would have forced overtime. New York had lost its previous two games.
Anthony scored 37 points and Stoudemire had 23 points and 12 rebounds. They combined to take 54 shots from the field and they made 25 of them.
Young led Washington with 24 points, hitting four from 3-point range.