Due to the various red flag stoppages, the majority of the field's final runs were impacted having used up the best of their tyres.
However, Drugovich was one of the few to return to the track after the third red flag which was caused by a system error.
Hitech Grand Prix's Marcus Armstrong was on provisional pole position going into the final minutes of the session but a stunning first sector from Drugovich - 0.5s up on Armstrong - meant pole for the Brazilian was a formality.
Drugovich took to the top with a 1m40.422s to move 0.6s clear of the rest of the field.
Richard Verschoor and Jack Doohan made the most of the cooler track conditions at the end of the session to complete the top three.
Armstrong was fourth ahead of Ralph Boschung, who looked favourite for pole without the red flag stoppages.
The Swiss was on course to beat Armstrong's provisional pole time but encountered traffic in the form of ART's Frederik Vesti at the final corner.
Liam Lawson was sixth for Carlin ahead of DAMS' Ayumu Iwasa, Trident's Calan Williams, Hitech's Juri Vips and Van Amersfoort Racing's Jake Hughes.
It was a disappointing session for Theo Pourchaire, whose car caught fire after 10 minutes of the session, resulting in the first red flag.
The second red flag was caused by Logan Sargeant's shunt in the middle part of the lap, leaving him down in 20th on the grid.
Cem Bolukbasi didn't qualify after crashing in practice and thus was taken to the hospital for pre-cautionary checks.