Brantley's bases-clearing double in the first inning gave the Indians a quick 3-1 lead and his solo shot in sixth put the Tribe ahead 6-1.
But the Tigers rallied to score the game's next five runs, tying it on a three-run clout by Torii Hunter in the top of the eighth.
That left it up to Brantley to again spark Cleveland, and he did so in the next half-inning on a game-deciding blast against Al Alburquerque (1-2) with Nick Swisher aboard.
The Indians left fielder finished 3-for-4 with five RBI and three runs scored while Carlos Santana and Lonnie Chisenhall each went deep as Cleveland salvaged the final contest of a three-game set and snapped Detroit's five-game winning streak.
Cody Allen (4-1) got the final out of the eighth to notch the decision and Chris Perez got his ninth save as the second-place Indians moved to within 2 1/2 games of the American League Central-leading Tigers.
Hunter finished with four RBI and Miguel Cabrera went 4-for-4 with a solo homer (his 28th of the season) and two runs batted in, raising his MLB-best batting average to .368. He also leads the majors with 90 RBI.