MILWAUKEE—Thanks to CC Sabathia and Ryan Braun, it suddenly didn’t matter that the Milwaukee Brewers spent much of the past month squandering a shot at their first playoff appearance since 1982.

Sabathia delivered a dominant four-hit complete game in his third straight start on three days’ rest, and Braun hit a tiebreaking homer in the eighth inning to lead the Brewers over the Chicago Cubs 3-1 Sunday.

Milwaukee won the NL wild card less than a half-hour later when the New York Mets lost to Florida 4-2—ending 26 years of frustration for the often-overlooked franchise. <...

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