Maholm (1-2) earned his first win as a Cub following a pair of rocky starts to begin the season, taming the Reds on one run on four hits over six frames.
The left-hander, who in January signed a one-year, $4.75 million deal with Chicago, walked three and fanned five.
Starlin Castro highlighted a four-run second inning with an RBI triple while Darwin Barney went 3-for-4 with a run batted in for Chicago, which evened its three-game set with Cincinnati at Wrigley Field.
Reds starter Mike Leake (0-2) was roughed up for 10 hits in 5 2/3 frames, yielding five runs.
Brandon Phillips got Cincinnati's only RBI.
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