Rodgers tossed for 308 yards, going 19-of-30 through the air, while Mason Crosby booted three field goals and John Kuhn added a rushing score for for the Packers (2-0).
Trailing 13-7 at halftime, Green Bay went ahead for good 3 minutes into the second half when Rodgers found Jennings on a 49-yard touchdown toss, and his 84-yard bomb to Nelson with 2 minutes left in the fourth iced the win.
Charles Woodson led Green Bay's defense with a pair of key interceptions.
Cam Newton was plagued by three turnovers in his second professional game, passing for 432 yards and one score for the Panthers (0-2).
Celebrity Couples of 2014 [PHOTOS]