The 26-year-old British number four fell 6-2 5-2 behind against the world number 97.
Evans then won three games in succession, forced a tie break and won the second set to level.
After a rain delay, Nishioka saw out the match in a third-set tie-break, winning in two hours 43 minutes.
Nishioka will face Ukraine's Alexandr Dolgopolov, the competition's fourth seed, in the next round.
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Britain's Dan Evans lost 6-2 6-7 (2-7) 7-6 (7-4) to Yoshihito Nishioka of Japan in the first round at the Atlanta Open.