Ramirez, who entered the game hitless in eight spring at-bats, took right-hander Mike Fiers' 2-1 pitch to left-center in the bottom of the second. He also walked, finishing the day 1-for-2, while Yoenis Cespedes came up empty in his three at-bats, striking out twice.
The A's entered the seventh down, 4-3, but they climbed ahead for good, beginning with Collin Cowgill's RBI single -- his sixth of the spring -- that tied the game. Jeff Fiorentino followed with a fielder's choice ground ball to Brewers first baseman Sean Halton, who threw home hoping to catch the running Eric Sogard. Caught in a rundown, Sogard safely crossed home plate for the go-ahead run, as interference was called on the play.
Brandon Moss and Anthony Recker also collected RBI hits in the frame.
For Milwaukee, Martin Maldonado hit his first home run of the Cactus League off lefty Brian Fuentes in the sixth, a three-run shot to left field. Fuentes surrendered four runs total, giving up three hits and a walk in just one inning of work.
Teammate Jarrod Parker fared better on the mound while making his third Cactus League appearance and second start, pitching 3 1/3 scoreless innings. The A's right-hander, heavily in the mix for a rotation spot, gave up two hits, walked three and struck out four.
Fiers, the Brewers' 2011 Minor League Pitcher of the Year, struck out four in two innings in his first Cactus League start.
Up next for the A's: The A's will enjoy their first off-day of the spring Wednesday, before resuming activity in Surprise, Ariz., for a 1:05 p.m. PT meeting with the host Rangers on Thursday. It marks the first Cactus League matchup of the spring for the division foes, who will see A's righty Bartolo Colon and Rangers southpaw Martin Perez on the mound. In two starts, Colon has given up a four runs with five strikeouts and no walks in a combined 6 2/3 innings.