Bailey (12-9) stifled Chicago on one run over 7 1/3 innings, allowing four hits while walking two and striking out four.
He exited after Bryan LaHair's run-scoring double in the eighth, and Sean Marshall then came in to record the final two outs of the inning.
Jonathan Broxton tossed a 1-2-3 ninth to pick up his third save for the National League Central-leading Reds, who claimed the first of a three-game series.
The Cubs' Justin Germano (2-8) was saddled with the loss, yielding three runs on five hits over five complete innings.
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