Baltimore won for the eighth time in 10 games, letting a five-run lead get away before coming up with the decisive run on Reimold's scratch base hit.
The Tigers have dropped two out of three and remained tied with Texas for the second-best record in the American League. Detroit and the Rangers are battling for home-field advantage in the opening round of the playoffs.
J.J. Hardy gave Baltimore a 2-0 lead in the third with a solo homer and the Orioles struck for three more in the fourth on a two-run blast by Adam Jones and a sacrifice fly from Reimold.
Detroit rallied to tie it thanks in part to Delmon Young's three-run homer during a four-run fifth.
Jones scored the winning run in the sixth, reaching on a lead-off single, stealing second, going to third on a groundout by Chris Davis and coming in on Reimold's single.