The Virtuosi driver was sixth after the first runs, with Juri Vips, who also topped practice for Hitech, leading the field.
Doohan then improved to fourth, before his third run, a 1m31.965s took him to the top of the timesheet as the quickest lap of the day so far.
As the field emerged on fresh tyres, DAMS driver Ayumu Iwasa was next to take provisional pole, 0.04s faster than Doohan.
But a flurry of flying laps saw Drugovich take the top spot before Marcus Armstrong and Liam Lawson demoted him, with Doohan then returning to the front of the field with a 1m31.641s to secure pole position.
Lawson will start second in Sunday’s feature race for Carlin, with Hitech’s Armstrong in third.
Lawson was early to top the timesheet, setting a 1m32.959s to lead early on in the 30-minute session, with Drugovich slotting into second 0.3s behind him, as Theo Pourchaire sat in 10th for ART.
Richard Verschoor was next to lead, but as the times fell, Lawson and Pourchaire went ahead before Vips set the fastest time of the early runs, a 1m32.018s, having benefitted from the tow from Luca Ghiotto, sitting in for Roy Nissany at DAMS.
Drugovich was knocked down to 10th by the tumbling times before improving to third on his next attempt, a 1m32.588s, with title rival Pourchaire just 0.009s behind him.
Doohan then set his fastest lap to demote the pair, with Logan Sargeant going third fastest for Carlin to push Drugovich to fourth.
There was a brief lull in the action as the field pitted for a new set of tyres, before emerging with eight minutes left on the clock.
Iwasa was next to go quickest with a 1m31.920s, before Drugovich, Armstrong, Lawson and eventually Doohan demoted him to sixth.
The Japanese Red Bull junior prompted yellow flags at the end of the session after crashing at the exit of Parabolica, having run across the gravel and hit the barrier, prompting a flash of flames before he walked away unharmed.
Verschoor will line up fifth for Sunday’s race, with Jehan Daruvala in sixth for Prema and Iwasa in seventh.
Frederik Vesti will start on pole for Saturday’s reverse grid sprint race, with Sargeant in second and Vips in third.
Pourchaire, who sits second in the standings 69 points behind Drugovich, will start 14th.
