The Marlins scored three runs through their first five batters and added a pair of runs in the second inning to allow Johnson to work with a comfortable lead.
Johnson (8-11) scattered four hits over seven innings. He allowed both runs -- on sacrifice flies from Ryan Braun and Norichika Aoki -- and walked three while striking out three.
Brewers' starter Marco Estrada (2-6) fell to the early Miami barrage. He gave up seven hits and four runs in five innings. He didn't walk a better and struck out five.
Bryan Peterson hit Estrada's third pitch for a double and came around on a Donovan Solano single. Jose Reyes followed with an RBI double and took third on a wild pitch that put him in position to score on a sacrifice fly by Greg Dobbs.
Braun had his sacrifice fly in the third inning and Aoki made the score 4-2 with his sacrifice in the seventh. Giancarlo Stanton and Dobbs had back-to-back doubles opening the Miami eighth with Donnie Murphy driving in Dobbs for the final run.
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