The Williams junior led practice earlier in the day, and stormed to the top of the timesheets early in the session with a 1m38.946s as the first driver to dip below 1m39s.
Once he took provisional pole, he was unmatchable, despite close challenges from Frederik Vesti (ART) and Prema Racing's Jehan Daruvala.
Sargeant improved midway through the session, shaving 0.5s off an already impressive lap time to seal his first pole position in the series.
It was Carlin's second pole position of the day, with the Farnham-based team also taking pole in FIA Formula 3, courtesy of Zak O'Sullivan.
Vesti set an early benchmark with a 1m39.611s, 0.3s quicker than second placed Jack Doohan (Virtuosi Racing).
Ayumu Iwasa was quick to challenge for second, with a 1m39.655s, before championship leader Felipe Drugovich went third with a 1m39.676s.
Juri Vips was next to take the top spot, with a 1m39.371s, but his tenure was short-lived as Sargeant put in his first flying lap of the session.
Daruvala slotted into second while most of the field pitted, setting a 1m39.115s, but he was soon demoted as the rest of the field returned with fresh soft tyres.
Vesti was quick to bounce back, snatching second back with a 1m38.539s, while Drugovich took third with a 1m38.553s to continue his title fight.
He had looked set to improve on his time, but a spin at Turn 18 ruined a last attempt.
Rival Theo Pourchaire (ART) will line up fourth on Sunday, setting an almost identical time to the Brazilian, who leads the standings by 49 points.
Sargeant's teammate Liam Lawson will line up fifth for the feature race, with Iwasa in sixth and Doohan in seventh.
After failing to improve on his earlier time, Daruvala finished tenth to take pole for Saturday's reverse-grid sprint race, with Enzo Fittipaldi of Charouz in second after struggling with the kerbs at Turn 3 early in the session.
Vips, who was dropped by Red Bull's Junior Team this week after using a racial slur but will remain at Hitech, will line up third for Saturday's race and eighth on Sunday.
