Roberts connected on a wind-aided blast to center with none out in the fifth, scoring Felix Pie and J.J. Hardy ahead of him to break a 1-1 tie and hand the Orioles a victory in their home opener.
Arrieta (1-0), meanwhile, limited the Tigers to one run on six hits over six frames, walking two and fanning three as Baltimore improved to 4-0 to start the season, a sharp turnabout from 2010 when they started 2-16 and finished 66-96.
Nick Markakis went 3-for-4 with a run scored and Matt Wieters collected an RBI single among his two hits for the O's.
Rick Porcello (0-1) yielded five runs on nine hits through five innings for Detroit, which fell to 1-3.
Will Rhymes drove in the Tigers' only run with a third-inning single.