Beal, who had missed nine games with a leg injury, heated up down the stretch, scoring 14 points in the fourth quarter.
The Wizards were trailing 101-100 with 5.9 seconds left when the Washington shooting guard drove past Beno Udrih for the key layup.
Carmelo Anthony had a final shot for the Knicks but his 3-point try at the buzzer bounced off the backboard.
Anthony poured in 32 points for New York, which finished 1-1 on a two-game homestand.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys