Kansas City's Jermaine Dye hit a two-run homer, his club-leading fifth, in the seventh inning off Justin Atchley to lift the Royals to a 3-2 victory over Cincinnati on Monday.
Kansas City has won three straight and five of six.
Rookie Dee Brown homered with two out in the Royals' first.
Griffey and Sean Casey consecutive doubles in the sixth off Dan Reichert to tie it at 1.
Griffey's double in the seventh scored Deion Sanders, who had walked, to give the Reds a 2-1 lead.
Jason Grimsley, who worked two innings in relief, picked up his second victory, while Roberto Hernandez worked a perfect ninth for his first save.
Mike Sweeney was a late scratch from the Royals' lineup with a bruised finger. Sweeney was hit by a pitch Sunday. Brown replaced him as the designated hitter.
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