The A's Jarrod Parker had pitching six shutout innings before the Mariners tied the score 1-1 on a one-out RBI single from Kendrys Morales.
The score stayed tied until, with one out in the bottom of the ninth, when Moss connected on a pitch from Carter Capps (2-3) and sent it over the center field wall for his 19th home run of the season.
Parker (9-6) ended up with a complete-game victory, allowing eight hits with no walks while striking out eight in helping the the second-place A's remain one-half game behind Texas atop the American League West.
Aaron Harang pitched seven innings of one-run ball for Seattle, which fell in the opener of a three-game series.
Celebrity Families of 2014 [PHOTOS]