Former Jacksonville State pitcher Donovan Hand, making his first big league start, allowed only two hits in 4 2/3 innings for Milwaukee. He struck out three and walked one in helping extend Atlanta's scoreless streak to 24 innings.
Burke Badenhop (1-3) entered after Hand walked Dan Uggla and got Chris Johnson to groundout to end the fifth.
Milwaukee has beaten Atlanta eight straight times at Miller Park, outscoring them 31-9.
Tim Hudson (4-7) lost his sixth straight decision, despite giving up just two runs and seven hits in six innings. He allowed RBI singles to Juan Francisco, in the fourth, and Aramis Ramirez, in the fifth inning.
The Braves have scored just 10 runs in Hudson's last nine starts. He has not won in nine starts, his worst winless stretch of his career since an eight-start stretch in 2002.
Rodriguez gave up one of the Braves' four hits in becoming the 25th closer in major league history to reach the 300-save milestone. He was aided by a barehanded pickup and throw by shortstop Jean Segura to get leadoff hitter Jordan Shafer.
Andrelton Simmons then singled, but Rodriguez got Jason Heyward to line out and Freddie Freeman struck out. After the strikeout, Rodriguez pumped his fist and pointed to the sky.
Rodriguez, who began the season out of baseball, was signed by Milwaukee May 16. He has converted all six of his save opportunities and has not been scored upon in 15 of his 16 appearances.
Milwaukee took a 1-0 lead in the fourth on Francisco's RBI single, then loaded the bases. But Hudson got Hand to groundout to end the inning.