A solo homer by Jack Cust in the top of the first inning had given Oakland a 1-0 lead and Sweeney's blast in the second made it 4-0. Daric Barton's bases loaded walk in the third gave Oakland a 5-0 advantage.
Winner Rich Harden (2-0) gave up an earned run and only four hits in seven innings with a walk and eight strikeouts.
Keith Foulke hurled a scoreless eighth before closer Huston Street gave up three runs in the bottom of the ninth.
Sweeney had two of the seven hits for the Athletics, who stopped a four-game losing streak.
Four Atlanta players had one RBI each. Mark Teixeira had two of the seven hits for the Braves, who have split their last four games.
Losing pitcher Tim Hudson (6-3) yielded five earned runs and five hits in five innings with five walks and three strikeouts.

