Trailing 4-1 in the sixth, the Brewers erupted for five runs, sending nine men to the plate to grab control of the game.
After loading the bases with none out against Nationals starter Taylor Jordan, Carlos Gomez narrowed Milwaukee's deficit to two runs with a sacrifice fly.
Fernando Abad (0-3) took the mound and was greeted by pinch-hitter Khris Davis with a run-scoring single, and Juan Francisco followed with an RBI double to tie the score.
Bianchi (three RBI) then came up and flared an 0-2 pitch into shallow center field, sending home Davis and Francisco with the go-ahead runs.
John Axford (5-4) was credited with the decision despite allowing a run in the sixth and Jim Henderson picked up his 15th save as the Brewers avoided a three-game sweep.