Mike Dunleavy scored a season-high 28 points for the Bucks, who snapped a six-game losing streak at home. İlyasova added 13 points, 11 rebounds and assist for Milwaukee.
Brandon Jennings took an inbounds pass with 6.8 seconds left and drove left of the lane, attempting a short jumper. It bounced off the rim, but İlyasova had position and tipped in the miss for the winning points.
Roger Mason Jr. then got an inbounds pass on the baseline for Washington but was called for traveling with 1 second to go without getting off a shot.
John Wall gave the Wizards a 118-117 lead when he drove around Jennings and scored on a running, 8-foot jumper with 6.8 seconds remaining.
Jennings finished with 14 points and 10 assists. Drew Gooden, who returned after missing four games with a sprained right wrist, had 15 points and 10 rebounds but landed hard on his back in the third quarter and did not return.
Trevor Booker scored 20 points while Wall and Jordan Crawford added 19 apiece for Washington.
Milwaukee opened a 22-point lead in the first half, but Washington hit six 3-pointers in the third quarter to get back in the game.
Dunleavy made a pair of free throws with 1:21 left to give Milwaukee a 117-114 lead before Booker drove the lane and scored on a dunk to bring the Wizards within 117-116 with 1:05 to go.
Dunleavy and Jennings each missed 3-point attempts on the next possession, but Booker missed a tip on the other end.
Jennings drove to the basket but dribbled the ball off his foot with 12 seconds left, giving Washington a chance to win the game.
Wall scored to give the Wizards a brief lead before İlyasova's clutch tip-in.
Washington erased a 14-point halftime deficit and took an 81-79 lead when Maurice Evans stripped Carlos Delfino and sprinted to a breakaway layup with 4:16 to go in the third quarter.
Luc Richard Mbah a Moute scored on a rebound with 1 second left to give Milwaukee a 92-89 lead after three quarters.
Milwaukee took its biggest lead, 55-33, on Dunleavy's 3-pointer with 5:35 left in the second. The Bucks ran off 13 consecutive points in the 30-12 run to open a commanding cushion.
Dunleavy had 16 points in the second quarter, including four 3-pointers, and Milwaukee took a 67-53 advantage into halftime.
Rose back to best as Bull beat Hornets
Elsewhere, Chicago's Derrick Rose showed he is back to full fitness by grabbing 32 points and nine assists to help the Bulls beat the New Orleans Hornets 99-95. Rose, who has missed 10 games this season with various injuries, scored six of the game's final eight points as the Bulls finished on an 8-0 run to hold off a late charge by the visiting Hornets.
Chicago also welcomed Richard Hamilton back to the lineup and had their season-opening starting five on court for the first time since Jan. 4. “We have to knock some of the rust off,” said Rose, who had appeared closer to top form in his two games back from injury before Sunday's All Star game.
Rose showed no signs of rust in his best performance in nearly a month, allowing Chicago (28-8) to tie idle Miami at the top of the Eastern Conference.
The win did not come easily, however, as New Orleans (8-26) erased a nine-point deficit midway through the fourth quarter and blitzed Chicago with a 13-0 run to grab a 95-91 lead with 1:25 to go before Rose took over.
The reigning league MVP cut the lead with two free throws, and later added a go-ahead jump shot with 19 seconds remaining before making another pair of free throws to cap the scoring.
Joakim Noah aided the home effort with 15 points, 16 rebounds and five assists. “You have to find different ways to win,” Bulls coach Tom Thibodeau told reporters. Chris Kaman recorded 17 points and 11 rebounds while Trevor Ariza added 16 points for the Hornets who are last in the Western Conference but are playing better as of late. New Orleans is 4-3 over their last seven games following a horrendous start to the season.
Tuesday's NBA results at a glance
Boston 86, Cleveland 83
Indiana 102, Golden State 78
Philadelphia 97, Detroit 68
Chicago 99, New Orleans 95
Houston 88, Toronto 85
Milwaukee 119, Washington 118
New Jersey 93, Dallas 92
Sacramento 103, Utah 96
Minnesota 109, LA Clippers 97