Brantley's clout in the third provided the only offense for the Tribe, but it was enough even after starter Fausto Carmona had to leave the game after only two innings and six relievers trooped to the mound to cobble the victory.
Carmona had hurled two scoreless frames when he suffered a right quadriceps strain while running out a bunt single.
Frank Herrmann (1-0) earned the victory with three shutout frames and Vinnie Pestano collected his first save with a scoreless ninth for the Indians, who clinched the series with their interleague rivals.
Cincinnati starter Homer Bailey (3-3) yielded three runs on eight hits over seven innings.
Joey Votto's solo homer in the eighth accounted for the Reds' only run.