The world champions have won all eight of their qualifiers so far to top Group C and are unbeaten in their last 17 games, dating back to their defeat against France in the Euro 2016 semi-finals.
Timo Werner capped a stunning display with two first-half goals as Germany cruised to 4-0 up at half time in Stuttgart.
It could have been 5-0 at the break after Toni Kroos' shot was stopped by a superb save from Norway's goalkeeper Rune Almenning Jarstein, who plays for Hertha Berlin, on the stroke of half time.
But Norway's defence was breached again just five minutes into the second-half when Schalke midfielder Leon Goretzka grabbed Germany's fifth goal when he headed home Draxler's cross.
Werner's replacement, the 32-year-old veteran Mario Gomez, headed home Germany's sixth on 79 minutes for his 31st international goal on his 71st appearance in the famous white shirt.
“That was a lesson for us,” admitted Norway coach Lars Lagerbäck, whose team are mathematically eliminated from World Cup qualification.
“Germany are a fantastic team, definitely one of the best in the world and they made it very, very hard for us.
“The best thing we can do is learn from them,” he added.
The defeat is the biggest margin suffered by Norway since a 9-0 humiliation at the hands of a Johan Cruyff-inspired Netherlands on November 1st 1972.
Norway striker Joshua King described the match as “the hardest day I have had on a football pitch.”
“It was embarrassing to be out there… I’m aware we were playing one of the best teams in the world, maybe the best in my opinion, but this does not look too good,” the AFC Bournemouth player told NRK, adding that world champions had “played around” the Norwegian team.
Jarstein called the defeat “heavy”.
“It’s a long time since I’ve felt so small. We all agree that this is embarrassing and painful. We have to face it, this was not good,” the goalkeeper told NRK.
Photo: Heiko Junge / NTB scanpix
Werner revelled in the victory in his hometown, having started his career with VfB Stuttgart, and came off to a standing ovation on 66 minutes against Norway.
The world champions raced into a 3-0 lead after just 21 minutes against the hapless Norwegians.
Arsenal midfielder Mesut Özil was a key figure, sparking the rout by finishing off a chance he created when he fired home Jonas Hector's cross for the opening goal after just ten minutes.
Paris Saint-Germain star Julian Draxler, on Germany's right wing, netted the second on 17 minutes when he turned in a tight space between defenders and fired home Özil's final pass.
Werner then slotted home Thomas Müller's final pass with a classic striker's goal on 21 minutes, and claimed his second by heading home Müller's cross on 40 minutes.