''It took a little bit of everybody to find a way to win this game,'' Bucks coach Mike Budenholzer said.
Westbrook had 29 points, 17 assists and 12 rebounds for his 179th career triple-double, but the Wizards still lost for just the fourth time in their last 17 games. He's just two shy of Oscar Robertson, whose 181 career triple-doubles are the highest recorded total in NBA history.
The Bucks led 127-124 when Antetokounmpo picked up his sixth foul with 1:54 left. They played the entire game without two-time All-Star Khris Middleton, who was out with a sore left knee after playing one night earlier in a 124-118 victory over Brooklyn.
They still found a way to win.
''It's big for us,'' said Donte DiVincenzo, who had 19 points. ''I think it's a big thing for us to come together and know we can pull it out in different ways.''
Pat Connaughton had 16 points and made a pair of 3-pointers in the final 90 seconds to answer Wizards baskets. Bryn Forbes added 14 and put the Bucks ahead for good by sinking a tiebreaking 3-pointer with 2:23 remaining.
Washington trailed by just two points with just over 30 seconds left when Holiday and Connaughton each blocked shot attempts by Daniel Gafford from under the basket. Gafford believed he was fouled.
''I should have really just passed up the ball at the end,'' Gafford said. ''Russ was right beside me. That would have been the smart play instead of trying to go up with that last layup attempt. It really just cost us the game, to be honest.''
Brook Lopez delivered a putback dunk that gave Milwaukee a four-point lead with 6.8 seconds left.
But the Wizards still nearly pulled it off.
Beal hit a 3-pointer that cut Milwaukee's lead to 135-134 with 5.3 seconds remaining. Westbrook got a steal in the final second, but Garrison Mathews' desperation shot from over 50 feet away didn't connect.
''We're putting ourselves in positions to win,'' Beal said. ''We're getting better with executing and closing out down the stretch, but obviously we can be better.''
Wizards: Westbrook has a league-leading 33 triple-doubles this season, including five in his last six games. The only time Westbrook missed out on a triple-double during this six-game stretch came Saturday when he had 42 points, 10 rebounds and nine assists in a 125-124 loss to Dallas. ... Rui Hachimura didn't play due to an illness unrelated to COVID-19. Anthony Gill replaced him and made his third start of the season. ... Washington's 43 free-throw attempts were the most by a Bucks opponent this season. ... Chandler Hutchinson left with a bruised left knee after playing three minutes.
Bucks: P.J. Tucker replaced Middleton in the lineup and made his first start since the Bucks acquired him from Houston on March 19. Tucker went scoreless in 20 minutes before leaving with a sore jaw. Tucker had started all 32 games in which he had appeared for the Rockets.
Wizards: Face the Toronto Raptors on Thursday in Tampa, Florida, as they try to avoid getting swept in the regular-season series. The Wizards fell to the Raptors 137-115 in Washington on Feb. 10 and 103-101 in Tampa on April 5.
Bucks: Host the Houston Rockets on Friday as they try to gain revenge after falling 143-136 in Houston on April 29.
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