Todd Jones (1-3) was called on to protect a four-run lead in the ninth, but with one out he gave up a single to Casey Blake and a walk to Travis Hafner. Victor Martinez followed with a home run, his second of the night, to cut the Indians' deficit to one.
Jhonny Peralta kept things going with a double and Nixon was intentionally walked, putting the potential winning run on base. Josh Barfield followed with a single that scored Peralta and tied the game, and then Dellucci singled to center on a 2-1 pitch to win it.
Martinez also homered in the fourth as Cleveland built its AL Central lead over the Tigers to 4 1/2 games.
The comeback gave the win to Robert Hernandez (3-1), who retired the final batter in the top of the ninth.
Detroit has lost seven of its last eight.