Knight also saved the Bucks in regulation by hitting a 3-pointer with 19 seconds to go that lifted Milwaukee into a tie.
The Bucks made up a four-point deficit in the final 90 seconds of the fourth period and won for just the second time in 15 games. Washington had been trying for its sixth win in seven contests.
Washington's Trevor Ariza was fouled attempting a 3-point shot with 42 seconds left in the overtime and he made all three free throws to pull the Wizards within one.
Knight then made his key jump shot that gave Milwaukee a 108-105 lead. His free throw with 11 seconds to play finished the scoring.
The Bucks overcame a 30-point show by Washington's John Wall, whose turnover with 12 seconds to go in overtime cost the Wizards a chance to tie the game.