Rodgers completed 17-of-30 pass attempts for 281 yards and one interception. Grant carried the ball 10 times for 85 yards in Green Bay's victory, the Packers' 19th straight dating back to last year's NFL Championship season.
Jordy Nelson hauled down three passes for 81 yards and a score for Green Bay. Donald Driver made four grabs for 75 yards in the one-sided win, during which the Packers set a franchise record for most points scored in a season.
The NFC North champs earned a first-round bye in the playoffs and kept alive their hopes for a perfect 16-0 season.
The news wasn't all good for the Packers, however. Their leading receiver, Greg Jennings, left Sunday's game on a cart after suffering a injury to his left knee early in the third quarter.
Carson Palmer was picked off four times for Oakland (7-6), which fell one game behind Denver atop the AFC West with the setback.