Rodgers completed 21-of-26 passes, threw for a touchdown and scored on a 1-yard, first-quarter run.
The two teams face each other again in an NFC wild-card contest next weekend.
Charles Woodson scored on a 45-yard, second-quarter interception return.
Ryan Grant scored once on 11 carries for 51 yards, and Donald Driver caught six passes for 65 yards for the Packers (11-5), who will enter the playoffs with seven wins in their last eight games.
Arizona played most of its defensive starters just one series and quarterback Kurt Warner played only the first quarter.
Back-up signal-caller Matt Leinart completed 13-of-21 passes for 96 yards with two interceptions.
Larry Fitzgerald scored on a 3-yard, fourth-quarter pass from No. 3 quarterback Brian St. Pierre, while Fitzgerald caught only three passes for 17 yards for the NFC West-champion Cardinals (10-6).
Celebrity Families of 2014 [PHOTOS]