Morales' 32nd homer of the season, a two-run blast, gave Los Angeles a 4-0 lead with two outs in the bottom of the third.
Maicer Izturis hit a two-run eighth-inning double, Mike Napoli hit a solo homer, and Vladimir Guerrero added an RBI single for the Angels -- who snapped a four-game losing streak and reduced their magic number for clinching the AL West title to two. The second-place Texas Rangers face elimination from the division race if they drop any of the four games in the series set to begin in Anaheim Monday.
The Rangers trail the Red Sox by six games in the AL wild-card chase.
Winner Joe Saunders (15-7) gave up three runs and seven hits in six innings.
Closer Brian Fuentes pitched a scoreless ninth, earning his 45th save.
Adam Kennedy, Matt Carson and Landon Powell each drove in a run for Oakland. A run scored on a wild pitch by Saunders in the seventh, while both Mark Ellis and Cliff Pennington had two hits for the Athletics, whose three-game winning streak ended.
The losing pitcher was starter Edgar Gonzalez (0-4).