Maholm (4-2) won his fourth straight start after a pair of rough outings to begin the season, handling the Braves on three hits over seven innings.
The left-hander issued three walks and struck out three, tossing 64 of his 95 pitches for strikes as Chicago took the rubber match of a three-game series at Wrigley Field.
James Russell hurled a scoreless eighth and Rafael Dolis collected his third save for Chicago, which improved to 5-3 in May.
Bryan LaHair drove in the game's only run with a seventh-inning single.
Atlanta starter Tim Hudson (1-1) absorbed the hard-luck loss, yielding just the one run on five hits in a seven-inning effort. He didn't issue a walk and struck out one Cubs batter.
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