Lowrie's blast in the third inning put Oakland ahead 5-1.
After Los Angeles narrowed the gap to 5-4 on Howie Kendrick's bases-clearing double in the next half-inning, Moss connected with Lowrie aboard in the fifth to break the contest open.
Tommy Milone (12-9) got the win despite yielding five runs on five hits over 5 1/3 innings for the American League West champion Athletics.
Angels starter Garrett Richards (7-7) was torched for seven runs on eight hits over 4 2/3 innings.
Kendrick finished 2-for-4 with four RBI for Los Angeles, which dropped the first of a three-game series.