New York had lost three out of four going into the all-star break, but the Yankees used the long ball and clutch pitching to breeze past the Athletics.
Cano broke a 1-1 tie with a three-run homer in the third inning and Rodriguez contributed a solo shot in the sixth.
Richie Sexson, released by Seattle last week and officially signed by the Yankees prior to the game, had an RBI single in his New York debut.
Mike Mussina (12-6) gave up nine hits in six innings, but struck out six to get the win.
The last 14 Oakland batters were retired in order.
Greg Smith (5-8) suffered the loss, allowing six runs on eight hits in 3 2/3.
Celebrity Families of 2014 [PHOTOS]