Ramirez scored a run in a two-run Brewers second inning.
Milwaukee starter Zach Greinke (6-2) went six innings, allowing nine hits with one walk and six strikeouts. He gave up one run on an RBI single by Dodgers starter Chad Billingsley that drove in Adam Kennedy in the second inning.
Billingsley (2-4) went six innings, giving up four runs on six hits with two walks and eight strikeouts. The Dodgers bullpen then limited the Brewers to one hit, until Carlos Gomez cracked a two-run home run off Todd Coffey in the top of the ninth.
It was the Brewers' first-ever four-game sweep at Dodger Stadium.
The Dodgers hit into three double plays, after hitting into four double plays Wednesday.