The Indians rallied to tie the game in the eighth inning, but Colorado won it in the ninth with a solo home run from Seth Smith off closer Chris Perez to power a 4-3 victory.
Travis Buck snapped an 0-for-24 skid with a two-out single that tied the game at 3 in the eighth.
Smith hit his second homer of the game in a 2-2 count off Perez.