Middleton, who finished with 40 points, hit a 3-pointer from the top of the key with 30.2 seconds left to five the Bucks a 135-132 lead.
After Beal made two free throws, Middleton was fouled with 7.8 seconds left and made both attempts from the line to make it 137-134 and Troy Brown, Jr.’s 3-pointer rimmed out at the buzzer.
Beal, one night after scoring a then-career high 53 points in a loss at Chicago, topped it with a 55-point effort that included 22 points in the fourth quarter and seven more in overtime.
Shabazz Napier added a season-high 27 points for Washington.
Giannis Antetokounmpo had 22 points and 14 rebounds before fouling out with 1:33 remaining in regulation for Milwaukee.
The Wizards rallied from 17 points down to take a 123-121 lead on Beal’s 3 with 1:01 remaining.
Eric Bledsoe‘s free throws tied it and after a miss by Beal, Middleton missed as well. Felipe Lopez blocked Rui Hachimura‘s layup attempt with 1:0 second left and Milwuaukee’s alley-oop toss at the buzzer failed.
Middleton had a career-high 51-points in the teams’ first meeting, a 151-131 Milwaukee win on Jan. 28.
The Bucks led 51-49 early in the third quarter when Middleton’s step-back jumper started a 14-2 run.
Washington rallied and Napier’s four-point play made it 102-93 with 9:29 left in the game, and his layup soon pulled the Wizards within seven. Middleton scored four straight points to push the lead back to double figures, but Beal scored 17 straight Wizards points and his 3 made it 119-116 with 2:15 left.
Bucks: Tied the Cincinnati Royals (81 games from Nov. 18, 1960 – Nov. 21, 1961) for the third longest streak of 100-point games in NBA history. … Bledsoe finished with 23 points and 10 assists. … Donte DiVincenzo had 23 points and 10 rebounds.
Wizards: Beal (4,107) passed Gus Johnson and Phil Chenier (tied with 4,057) for fourth place all-time in field goals made for the franchise. … Beal has nine games of 40 or more points, tied with Gilbert Arenas for fourth-place all-time for the franchise. … Have forced 20-plus turnovers in five straight games.
Bucks: At the Toronto Raptors on Tuesday night.
Wizards: Host the Brooklyn Nets on Wednesday night.