"We made this game a lot harder than it should have been," said Washington's John Wall, who scored only nine points and missed 10 of 14 shots.
The Wizards opened a 71-43 lead in the second quarter against Milwaukee (12-50), the NBA's first team to lose 50 games. But the Bucks cut the deficit to 104-101 on a pair of free throws by Ersan Ilyasova with 2:13 to go.
"It's unfortunate that we have to learn a lesson from this game," said Martell Webster, who scored 15 points after missing two games with a sore back.
"No disrespect to that team that's over there. Milwaukee's just is in a dysfunctional state," he said. "These are games that we know we're supposed to win by a large margin. In this league, you have to kick them when they're down."
After Ilyasova pulled the Bucks within three points, Beal then scored on a driving layup and hit a baseline 3-pointer to give the Wizards a 109-101 lead with 2:01 left.
"That kind of stemmed the tide a little bit," Washington coach Randy Wittman said. "Those were big baskets."
Washington won for the eighth time in nine games.
Wall, Washington's leading scorer at 19.9 points per game, had 13 assists and seven turnovers. Trevor Ariza scored 17 of his 26 points in the first quarter as the Wizards built a big lead.
"They weren't really missing (shots), and we didn't really help ourselves because of a lack of hustle," said Milwaukee's Brandon Knight, who scored 25 points.
After dominating the first half, the Wizards missed 13 of 17 shots in the third quarter. Washington scored only 10 points and had seven turnovers in the period.
"We took shortcuts defensively, we just stopped playing," Wittman said.
Washington made 29 of 43 shots in the first half and took its 71-43 lead on Beal's 3-pointer with 2:24 left in the second quarter. The Wizards led 75-53 at halftime, a season high in points for the first half.
Milwaukee scored the first 12 points of the third quarter to pull within 75-65, but Ariza scored on a driving layup with 4:57 left to snap the Wizards' scoring drought.
Washington scored the final four points of the first quarter and then outscored Milwaukee 30-12 to open the second quarter, opening a 66-39 lead on Ariza's 3-pointer with 4:14 to go in the half.
But the Wizards missed their first nine shots of the second half to let Milwaukee back into the game.
"We kept cutting into the deficit but leads like that are just very, very hard to overcome," Milwaukee coach Larry Drew said.
Ilyasova returned from a one-game suspension for punching Sacramento's Reggie Evans on Wednesday night and scored 13 points in 27 minutes. His teammate, O.J. Mayo, missed the game after being given a one-game suspension for punching New Orleans' Greg Stiemsma on Friday night.
Ariza made six of eight shots in the first quarter to score 17 points and give Washington a 36-27 lead. Trevor Booker made one of two free throws to give the Wizards the lead for good, 16-15, with 5:33 left in the first quarter.
The game marked the return to Milwaukee of forward Drew Gooden, who signed a second 10-day contract with the Wizards on Saturday. Gooden, who signed a five-year, $34 million contract with the Bucks in 2010 but was released on an amnesty provision before this season, scored 13 points in 16 minutes off the bench.
NOTES: Ariza went to the court hard with 6:16 left in the first quarter. He stayed on the ground for about a minute before rising and walking to the bench. . The Wizards previous first-half high was 74 points against Philadelphia on March 1. . The Wizards have won 14 of their last 20 road games.