Hanson (7-3) put only one runner on base during the first five innings and worked his way out of a sixth-inning jam en route to his fourth straight victory. He struck out six and did not walk a batter.
Troy Glaus had a two-run single during Atlanta's three-run third and Eric Hinske added a solo homer in the sixth. The Braves took a 6-0 lead into the ninth before the Rays scored twice against Jonny Venters.
Martin Prado went 3-for-5 with an RBI and boosted his league-leading hit total to 95.
Wade Davis (5-7) suffered the loss, giving up three runs on seven hits in five innings.
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