J.J. Hardy homered in the sixth ahead of Braun's big hit, which came off Aaron Heilman (2-2) after the Cubs reliever entered and threw five straight balls to walk Corey Hart and fall behind Braun.
Braun admired his opposite-field drive for a moment, then stuck his tongue out in a Jordan-esque display while slapping hands with first base coach Ed Sedar. Milwaukee has won four of five and 13 of the last 17.
It was an unfortunate end for the Cubs, who sent reserve outfielder Joey Gathright to Triple-A and traded him to Baltimore for utility player Ryan Freel because of the lack of infield depth.
That move allowed the Cubs to call-up pitcher Randy Wells, who threw five scoreless innings in his first major league start. Wells is in Carlos Zambrano's spot in the rotation with the ace recovering from a hamstring injury.
Milton Bradley homered in the fifth off Brewers starter Dave Bush and Alfonso Soriano's sacrifice fly in the sixth gave Chicago a 2-0 lead as Wells stranded six Brewers in the first three innings.
But Hardy answered with a solo homer off reliever Angel Guzman in the bottom of the sixth to cut the lead to 2-1 and the Cubs couldn't scratch across a run with one out and the bases loaded in the eighth.
Reliever Mitch Stetter (2-0) earned the win by getting the only batter he faced out, forcing pinch-hitter Geovany Soto to ground out to end the threat, and Trevor Hoffman finished with a perfect ninth for his fifth save.
Ramirez went down in the third inning diving for Braun's grounder and immediately clutched his left arm.
