Behind Quartararo and ahead of Marc Marquez in qualifying were Francesco Bagnaia and Alex Marquez.
Bagnaia has missed out on pole by a combined margin of under 0.1s over the past two weekends.
Second marked his equal best qualifying this morning after taking the same result in Q2 last week in Mugello.
The Italian has won each of the last three Dutch TTs in the MotoGP class, and won last year's Sprint, too.
Marquez, on the other hand, has never finished on the podium in any MotoGP race at Assen. That was also true in Mugello, though, and Marquez has been more or less as competitive as ever this weekend.