The 413-foot milestone was Griffey's seventh homer of the season. He is first among active players with 600 homers, with home-run king Barry Bonds (762) and Sammy Sosa (609) not currently a part of a major league roster.
Cincinnati catcher Paul Bako hit two home runs and drove home five runs in the victory.
Edinson Volquez (9-2) got the win after pitching six innings with three runs allowed on three hits with five walks.
Jeremy Hermida drove home a pair of runs for the Marlins, who committed three errors and fell to four games behind National League East-leading Philadelphia.