Rodgers -- the first quarterback other than Favre to start for Green Bay in 16 years -- completed 18-of-22 passes for 178 yards and a touchdown and ran for 35 yards and another TD for the Packers (1-0).
Ryan Grant rushed for 92 yards on 12 carries and Greg Jennings caught five Rodgers' passes for 91 yards.
Favre, who changed his mind about retiring, was traded to the New York Jets Aug. 7. Last season, Favre led the Packers to the NFC championship game where they lost to eventual Super Bowl-champion New York Giants 23-20.
Minnesota's Tarvaris Jackson, who sat out the final two pre-season games with a sprained knee, engineered two fourth-quarter touchdown drives, finishing 16-of-35 for 178 yards with a touchdown.
Adrian Peterson, the 2007 Rookie of the Year, ran for 103 yards and a TD and Sidney Rice caught a 23-yard touchdown pass for the Vikings.