Rodgers went 21-of-29 through the air for 283 yards, good for a passer rating of 142.7 in his first career five-TD game. He set an NFL record with a rating of above 100 for the 13th time this season.
Jordy Nelson made six grabs for 115 yards and two touchdowns, including a 55-yarder midway through the third period. James Jones also caught a pair of scoring strikes for Green Bay (14-1), which bounced back from its only defeat of the season.
The victory clinched the best record in the NFC for the Packers and assured them a first-round bye and home field advantage throughout the playoffs.
McCown completed 19-of-28 passes for 242 yards and a touchdown. He was intercepted twice.
Swim Week Miami Beach 2014 [PHOTOS]