The Brewers opened a six-game trip with their eighth straight road victory after losing five straight games at home, including four in a row to the Chicago Cubs.
With the Cubs' 3-0 loss to Pittsburgh on Friday, the Brewers moved four games behind Chicago in the NL Central.
Suppan (6-7) gave up only five hits with the three walks and one strikeout. Brian Shouse and Guillermo Mota each pitched an inning to complete the Brewers' fifth shutout.
It was Suppan's second dominant effort in three starts against Atlanta this season. He gave up four hits and overcame five walks in eight scoreless innings in a 1-0 win over the Braves on May 28 in Milwaukee. He allowed four runs in a 4-2 loss in Atlanta on June 25.
Suppan loaded the bases with three walks in the fourth but escaped the jam when pinch-hitter Greg Norton hit an easy fly ball to left field.
It was the only time the suddenly punchless Braves threatened. The Braves, who have lost six of seven, again were without catcher Brian McCann, who missed his fifth straight game while recovering from a slight concussion but was given medical clearance before the game for use as a pinch-hitter.
The Brewers scored six runs in the first three innings to knock left-hander Chuck James out of the game. James (2-4), recalled from Triple-A Richmond for the start, gave up six runs on six hits and four walks in 2 2-3 innings.
Rickie Weeks led off the game with an infield single, moved to second on J.J. Hardy's walk and scored on Ryan Braun's double to center. Corey Hart's fly ball to right drove in Hardy for a 2-0 lead.
