Rodgers completed 23-of-33 passes and threw a TD pass to John Kuhn, who also scored on the ground for the Packers.
Green Bay now moves on to play at San Francisco next week.
Ten Green Bay receivers made a catch against the Minnesota defense, setting an NFL playoff record as the Packers avenged a loss to the Vikings in last week's regular-season finale.
The Vikings played the contest without quarterback Christian Ponder, who was placed on the inactive list shortly before the game with a sore throwing elbow.
Backup Joe Webb started and was inconsistent, completing 11-of-30 passes for 180 yards, an interception and a touchdown.
NFL MVP candidate Adrian Peterson was limited to 99 rushing yards on 22 carries for Minnesota.