That brought up Ludwick, who shot a 2-2 pitch into the left-field corner, scoring both runners for a 3-2 Reds lead.
Bronson Arroyo (8-7) earned the win with eight solid innings, yielding a pair of runs on five hits while walking one and striking out four.
Aroldis Chapman fanned two during a 1-2-3 ninth for his 27th save as the National League Central-leading Reds won their second straight following five consecutive losses.
David DeJesus drove in both Cubs runs.
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