Griffey's second-inning blast moved him past Hall of Famer Frank Robinson for sole possession of sixth place on the all-time home run list with 587. Griffey, who had four RBI for the night, has 24 homers this year.
Cincinnati starter Bobby Livingston (2-0), who was recalled from Class AAA Louisville earlier Monday, went five innings and allowed two runs on eight hits. Livingston also went 4-for-4.
Kyle Davies (4-8) started for Atlanta and failed to record an out. After allowing two runs on two hits and three walks, Davies was replaced by Oscar Villarreal in the first. Villarreal didn't fare much better, giving up four runs on five hits in three innings.
Yunel Escobar had three hits for the Braves, who lost for just the second time in their last nine games.
'Happy' fan videos make Pharrell cry [VIDEO]
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend