The visitors had the opening possession of the game, but could not find their way into the endzone, forcing Mason Crosby to take a field goal to open the scoring.
Crosby was involved again before the break, edging Green Bay ahead with his third field goal of the day, before Rodgers finally got the ball in the endzone after a number of penalty flags slowed the play, connecting with Randall Cobb for the score.
Minnesota soon closed the gap after the break as Rudolph hauled in a 33-yard pass from Bridgewater, setting up Adrian Peterson for a six-yard dash to the endzone.
Green Bay quickly got back into a strong field position though, with Jones hauling in a 37-yard catch down the sideline, before getting his hands to the ball again in the endzone.
To put themselves two scores clear, the Packers went for a two-point conversion, with Rodgers picking out Jones for the third time in four plays to put the visiting side 14 points up early in the fourth.
Bridgewater looked for options to get Minnesota back in the game, but kept hold of the ball for too long, allowing the Packers to sack him on consecutive plays, forcing another punt from the Vikings.
Green Bay tried to run the clock down in the final six minutes of the game, before Crosby lined up a 52-yard field goal, splitting the uprights to maintain his 100% record in the game.
The result moves the Packers back to the top of the NFC North, leapfrogging today's opponents.