Hudson (2-1) got the big outs when he needed them in the 98-pitch effort, issuing a pair of walks while striking out three for the Braves, who earned a split of their two-game series against Cincinnati.
Martin Prado went 3-for-4 with a run-scoring single that ignited a decisive four-run outburst in the third inning.
Johnny Cueto (4-1), the major-league leader in ERA coming into the contest, was saddled with his first loss. The Reds right-hander was tagged for six runs (five earned) on eight hits through four full innings.
Ryan Hanigan drove in Cincinnati's only run.