Braves starter Jo-Jo Reyes had given up just two hits and retired 14 batters in a row before walking J.J. Hardy on four pitches leading off the eighth.
Blaine Boyer replaced Reyes, and Jason Kendall's sacrifice bunt gave the Brewers their first runner in scoring position. After pinch-hitter Joe Dillon struck out, Weeks hit his second triple of the season down the left-field line.
Salomon Torres pitched a perfect ninth for his fourth save in six opportunities, completing the four-hitter and giving the Brewers their fourth win in five games. Milwaukee will try to finish off a three-game sweep of the Braves on Thursday.
Suppan (3-4) allowed all four hits in a season-high eight innings. He also had a season-high seven strikeouts and managed to pitch around five walks to beat Atlanta for the first time in his career.
Reyes (2-3) finished with nine strikeouts in seven-plus innings, both career highs. He gave up only two hits and walked three.
It was Ned Yost's 400th career victory as manager of the Brewers, who won for the first time this season when scoring fewer than three runs.
The Braves had a good chance to score in the fifth when Yunel Escobar singled to left and moved up on Kelly Johnson's sacrifice. Suppan walked the hot-hitting Chipper Jones to get to Mark Teixeira, who flied out to center to end the inning.
Jones extended his hitting streak to 10 games with a single in the third. He has a hit in 43 of 49 games this season.
Atlanta stranded seven runners through the first five innings, and had two runners on base in four of the first five innings.
Milwaukee Brewers' Corey Hart (1), Ryan Braun, and Mike Cameron, right, celebrate after the ninth inning of a baseball game against the Atlanta Braves on Wednesday in Milwaukee. The Brewers won 1-0. / photo: Associated Press
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