The victory was the 2,010th of Joe Torre's managerial career with the Yankees, moving him into ninth place on the all-time list ahead of Leo Durocher.
Alex Rodriguez contributed three hits, one of them a double that drove in a run.
Mussina (4-5) had lost his previous two outings, but provided a much-needed effort in helping New York win for only the second time in nine games.
Joe Kennedy (2-6) was the victim of little support, as he gave up two runs on seven hits over six innings. Oakland has lost seven out of eight.
Both of New York's runs came in the first when Rodriguez doubled home Hideki Matsui and then scored on Jorge Posada's single.
Celebrity Families of 2014 [PHOTOS]