Rodgers found Randall Cobb for a pair of scores, finishing the game 14-of-30 through the air for 218 yards with an interception.
His 72-yard TD pass to Tom Crabtree in the third quarter blunted an Arizona comeback bid and all but sealed the victory.
The Packers (6-3) are expecting to use the week off to help heal injuries to such as key players as linebacker Clay Matthews (hamstring), wide receiver Jordy Nelson (ankle) and offensive tackle Bryan Bulaga (hip).
The Cardinals (4-5), meanwhile, remained mired in a slump, dropping their fifth straight despite 306 yards on 23-of-46 passing from John Skelton.
He finished with an interception and a touchdown in the loss.
Celebrity Couples of 2014 [PHOTOS]