Lynn (1-0) baffled the Reds on one run in six innings, allowing four hits while issuing just one walk as St. Louis evened its three-game series.
Adams' blast in the sixth inning came as he was pinch-hitting for Lynn and erased a 1-0 deficit.
Cincinnati starter Bronson Arroyo (1-1) took a perfect game into the sixth inning but then fell apart, eventually allowing four runs on five hits while striking out two.
Shin-Soo Choo led the Reds' offense with two singles.
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