It was Miller's first MotoGP pole position in four years as the Australian finished 0.015 seconds ahead of Ducati team mate Francesco Bagnaia.
"We were able to get the job done. Lap after lap, just feeling it out. To do that lap time in these kind of conditions, I was pretty happy with that," Miller said in a post-race interview.
"It's my second pole in MotoGP, it's been a long time since the last one so it's an awesome feeling, especially to do it here at home for Ducati."
Second-placed Bagnaia will start fifth on the grid in Sunday's race due to a three-place grid penalty he picked up in the first free practice session for riding slowly on the racing line, causing a dangerous situation for other riders.
Gresini Racing's Enea Bastianini came third, while MotoGP Marco Bezzecchi finished fourth for Mooney VR46 Racing Team after being the fastest rider in the first qualifying session.
Quartararo will be joined on the third row by championship contender Aleix Espargaro, who was ninth for Aprilia Racing.
