Hart underwent arthroscopic knee surgery on March 6.
Alex Gonzalez had three hits, including a two-run home run, for the Brewers.
Brewers starter Randy Wolf threw four innings and allowing one run on two hits, striking out six.
Milwaukee reliever Amaury Rivas did not retire a batter in the eighth inning. He allowed four runs and five hits.
Arizona minor leaguer Evan Frey had the big blow in the eighth, a three-run triple.
Diamondbacks starter Josh Collmenter tossed three hitless innings, surrendered an unearned run, walked and hit a batter and struck out one.