Villar lined an 0-2 pitch into left field off Casey Kelly (0-2), who had been scheduled to start for the Braves on Saturday. Instead, he wound up going four innings after the Braves used up their entire bullpen by the end of the ninth.
Atlanta dropped to 2-19 at Turner Field.
Kelly escaped a bases-loaded jam in the 12th but couldn't do the same after Milwaukee did it again with no outs in the 13th. Martin Maldonado grounded into a force at home to give the Braves a brief reprieve, but Villar came through.
Michael Blazek (3-1) picked up the win for the second night in a row. Carlos Torres earned his first save.
