The current champions went 3-0 up within the first 22 minutes, and it was Ozil who opened the floodgates with a first-time strike from inside the box.
Toni Kroos came close to doubling Germany's lead two minutes later when the Real Madrid midfielder unleashed a shot in the danger area, but his attempt went wide of the post.
Ozil was involved in the third goal when his pass to Julian Draxler ended with the ball nestling into the bottom corner, which put Norway on the ropes for the rest of the match.
Goals continued to fly into the net, and one man in particular who shone was Timo Werner, who scored twice - the first was a simple tap-in, while the second came from a close-range header.
Kroos tried to join the party with a shot aiming for the bottom left corner, but Rune Jarstein stretched across to make a save, although the same could not be said five minutes later when Leon Goretzka leapt into the air to head home a fifth goal.
Joachim Low's team have won all eight of their qualifiers.