Trailing 6-3 entering the frame, the Tigers scored four times off Reds relievers Lyle Ondrusek and Aroldis Chapman (4-2), stunning Cincinnati and earning a win in the rubber match of their three-game series.
Chapman allowed a single to Brennan Boesch with none out to load the bases in the eighth, then hit Matt Young with a pitch to force in a run.
Jackson (2-for-3, three RBI) followed by lining a pitch down the third-base line that was touched by a fan for a ground-rule double, allowing the tying runs to score.
Chapman then uncorked a wild pitch with Miguel Cabrera at the plate, enabling Young to scamper home with the decisive tally.
The rally made a winner of Brayan Villarreal (3-1). Jose Valverde picked up his 12th save for the Tigers.
Todd Frazier went 2-for-4 with a two-run homer and four RBI for the Reds. Zack Cozart and Devin Mesoraco each added solo shots for Cincinnati, which fell into a first-place tie with Pittsburgh atop the National League Central.