Davis (3-for-5) unleashed a two-run blast in the fourth inning, triggering a six-run outburst that broke open the game, and added a two-run homer in the ninth to cap Baltimore's 17-hit attack.
Adam Jones chipped in three RBI as Baltimore picked up its eighth victory in 11 games overall.
Chris Tillman (8-2) notched his fourth win in four starts, yielding three runs on seven hits over five innings. He issued three walks and struck out one.
Tigers starter Rick Porcello (4-4), meanwhile, was lit up for six runs on nine hits over six frames.
Matt Tuiasosopo drove in two runs for Detroit.