Ilyasova's game-winner came after John Wall's off-balance floater had given the Wizards a one-point lead 4 seconds earlier.
Washington had one last chance to go for the win but Roger Mason Jr. was whistled for traveling, wrapping up the Bucks' victory.
Ilyasova finished with 13 points and 11 rebounds, while Mike Dunleavy poured in a season-high 28 points off the bench as the Bucks snapped a six-game home losing streak.
Wall turned in an all-around performance of 19 points, 15 assists and five rebounds for Washington, and Trevor Booker pitched in with a double-double of 20 points and 11 boards.
The Wizards suffered their fifth consecutive loss.