Morales' three-run shot in the first inning gave the Angels all the offense they would need behind Jered Weaver's 6 2/3 shutout innings.
It was the Angels slugger's first homer since he hit a walk-off grand slam May 29, 2010, and then broke a leg while celebrating with teammates at home plate.
Morales finished 3-for-4 with four RBI as Los Angeles took the opener of a four-game series against the Athletics.
Weaver (2-0) yielded five hits and one walk while striking out six to earn the win.
Oakland starter Brandon McCarthy (0-2) was roughed up for five runs on 11 hits over seven-plus innings.