The Athletics were trailing 4-2 with one out in the ninth against Mariners closer Tom Wilhelmsen when Josh Reddick walked and Josh Donaldson then deadlocked the contest with two-run clout.
In the 10th, Coco Crisp led off with a single against Oliver Perez (1-3) and one out later Stephen Pryor came on to pitch. Yoenis Cespedes worked him for a base-on-balls and Moss followed with a decisive, three-run blast to right field.
Moss finished with five RBI and Grant Balfour (3-2) earned the victory for the A's, who logged their 14th walk-off win of the season and reduced their magic number for clinching a playoff spot to three games.
Michael Saunders hit a two-run homer and Kyle Seager added a solo shot for the Mariners.