Hudson (4-2) gave up three hits and walked no one. It was his 22nd career complete game.
The Braves, who halted a four-game losing streak, got a two-run homer from Brian McCann in the fourth inning.
The loss went to Edinson Volquez (4-1), who gave up just four hits, walked two and struck out nine over six innings. Volquez also had one of the Reds' three hits.
Cincinnati lost its third in a row.
Reds centerfielder Corey Patterson misplayed a fly ball for an error in the fourth, allowing Chipper Jones to reach second base. One out later, McCann hit his sixth homer of the year -- a towering shot to right.