Griffey, who extended his hitting streak to 14 games, now has 534 home runs in his career and is tied for 13th with Jimmie Foxx on the all-time list.
Cincinnati has won four in a row and eight of its last 10. Sean Casey added a two-run homer.
Winning pitcher Luke Hudson improved to 6-6. He has won five of his last six starts.
Humberto Cota and Craig Wilson had one RBI apiece for Pittsburgh, which has lost five straight and 10 of its last 13.
Loser Kip Wells sank to 7-14 and now is 1-6 in his last nine starts.
Notable deaths of 2014 [PHOTOS]