Mueller took advantage of shoddy Norwegian defending to give the title holders an early lead and headed the third goal on the hour of the European Group C game.
In between, he produced a superb pass to set up Joshua Kimmich for his first international goal.
Germany made light of the absence of Jerome Boateng, Mario Gomez and Andre Schuerrle, plus Lukas Podolski and Bastian Schweinsteiger who both have retired from international football.
They enjoyed 68 percent of the possession, spent nearly the entire game inside the Norway half and goalkeeper Manuel Neuer, given the captaincy in place of Schweinsteiger, did not have to save a single shot on target.
"We controlled everything, we didn't allow Norway to get into the game and we didn't allow them any scoring chances," said Loew. "I'm happy with the performance.
"It was good for Mueller to get the goal and good for us," he said, then added jokingly: "I would have preferred him to have scored some goals in the European championship."
Norway, who beat Germany 1-0 away in a friendly in 2009 when the teams last met, lacked ambition from the outset but any plans they may have had of frustrating the visitors were quickly torpedoed.
The home defence twice failed to clear the ball and Mueller, who failed to hit the target in Euro 2016, managed to score with a deflected shot despite being off-balance in the 15th minute.
A lucky bounce gave Norway a rare opening but Joshua King, given a free shot on goal, sent his effort high and wide.
Germany, who had not played Norway in a competitive game since 1953, scored again on the stroke of halftime when Mueller threaded the ball to Kimmich who drove it into the far corner, leaving two Norway defenders on the ground.
The second half continued in a similar vein and it was no surprise when Mueller added a third, heading in from Sami Khedira's cross for his 34th international goal.
It was the perfect start for Germany in what appears to be one of the easiest qualifying groups. They were given another boost when the Czech Republic, who were expected to be their nearest rivals, dropped two home points in a 0-0 draw with Northern Ireland.
In the group's other game, Ruslan Gurbanov's goal on the stroke of halftime gave Azerbaijan a 1-0 win at minnows San Marino.
(Writing by Brian Homewood; Editing by Rex Gowar)
