The Wizards led by double figures midway through the first quarter, were ahead 56-38 at halftime, and pushed the margin to 27 points in the third quarter.
Cleveland trailed 86-71 midway through the fourth before Kyrie Irving scored 11 straight points to cut the deficit to four points with 2:56 remaining.
Marcin Gortat's two free throws with 1:16 left extended the lead to 92-86, and Beal added two free throws with 32.8 seconds remaining to put the game away.
Irving scored 28 points, including 18 in the final period, to lead Cleveland, which has dropped four of five.
Washington, which broke a four-game losing streak on Tuesday by rallying from a 16-point deficit to defeat Minnesota, has won two straight for the second time this season. The Cavaliers beat the Wizards in overtime on Saturday when Irving matched his career high with 41 points.
Washington raced to a 21-9 lead in the rematch, forcing Cleveland coach Mike Brown to use two timeouts in the first seven minutes. The Wizards built a 14-point lead and shot 13 of 26 in the quarter.
The margin reached 50-32 on Wall's three-point play with 3:15 remaining in the second quarter, marking the first and only time the Wizards went to the foul line in the first half.
Washington built a 73-46 lead midway through the third quarter before the Cavaliers reserves cut into the margin.
Both teams are searching for ways to put an end to their disappointing starts. Cleveland's players held a meeting after last week's 29-point loss to Minnesota. The meeting reportedly got heated, but several players said no punches were thrown.
Shooting guard Dion Waiters, who missed the next two games with the flu, returned to practice Monday, but lost his starting job to Miles while he was gone.
Brown said before the game he was pleased with his new lineup, but the switch lasted less than three minutes when Miles left the game with a strained right calf and was taken to the locker room. Waiters entered the game with 9:27 left in the first quarter.
Anthony Bennett, the No. 1 pick in the draft, entered the game to begin the fourth quarter with the Cavaliers trailing 80-59. Bennett, who is 5 for 37 from the field, shot an air ball on a 3-point attempt.
Cleveland center Andrew Bynum, who said earlier this month he is considering retirement as he comes back from surgery on both knees, scored two points and had one rebound in 12 minutes.
The Wizards broke a four-game losing streak against the Cavaliers. ... Cleveland C Tyler Zeller (sprained right ankle) was inactive. ... F Trevor Ariza (strained right hamstring) and F Al Harrington (sore right knee) missed the game for Washington. ... Cleveland, which is 1-6 on the road, plays at New Orleans on Friday and at San Antonio on Saturday. ... Wall had nine assists after tying his career high with 16 on Tuesday.
Officials said after the Oklahoma City Thunder's 98-97 win over the San Antonio Spurs on Monday night that they should have called an offensive foul on a controversial late-game sequence.
ESPN's Brian Windhorst discusses the Cavaliers Game 1 win over the Hawks and how Cleveland showed signs of fatigue late in the game that allowed Atlanta to keep pace until the end.
Russell Westbrook and Kevin Durant combined for 57 points, but the story of Game 2 occurred in the final seconds, when Dion Waiters elbowed Manu Ginobili and turned the ball over. San Antonio was unable to score on the possession and lost 98-97.