Both teams scored three times in the third inning, leaving the Angels with a 4-3 lead, and Nick Swisher tied it in the fourth with a home run.
It remained a 4-4 contest until the eighth, when Joba Chamberlain (0-1) gave up a leadoff single to Hideki Matsui and a home run to right by Morales.
Fernando Rodney (2-0) picked up the victory by working the top of the eighth. Brian Fuentes threw a perfect ninth for his second save.
The Yankees lost their second straight and Los Angeles won for the first time in three tries.
Morales also drove in the first Los Angeles run with an infield single in the opening inning.