The ART driver was yet to set a time with 10 minutes remaining after having had several laps deleted for exceeding track limits, for which he was also shown the black and white flag.
The Mercedes junior then set a 1m14.123s in the second set of runs to go quickest by 0.035s, taking his first series pole, having secured his first win in the Baku sprint race.
Despite Jack Doohan’s early advantage and a strong fight from championship leader Felipe Drugovich, Vesti managed to hold onto the top spot, with Hitech’s Vips and Sargeant (Carlin) demoting the pair to fourth and fifth.
Ayumu Iwasa was first to set a quick time for DAMS, with a 1m15.287s early in the session to lead the timesheet.
Drugovich (MP Motorsport) knocked him off the top spot with a 1m15.022s, before he was toppled first by Sargeant, then by Doohan, who was almost 0.5s quicker.
The Virtuosi Racing driver led for much of the session, with Sargeant running in second before his time was deleted, demoting him to seventh.
Amaury Cordeel, returning from a race ban at Silverstone, shot up into second place for Van Amersfoort Racing as he ran while others pitted, setting a 1m14.457s to slot in behind Doohan.
The times tumbled in the final few minutes, despite heavy traffic as drivers prepared for their final runs.
Drugovich took the top spot before it was reclaimed by Doohan, who was then surpassed by Vesti’s best time.
Doohan and Drugovich both had times deleted, with Vips sealing second and Sargeant, who took his first win at Silverstone, in third.
Iwasa, who was last over the line, improved from sixth to fourth with his final lap, a 1m14.307s, while Drugovich and Doohan will start fifth and sixth after their late lap deletions.
Cordeel settled for seventh after others improved, with Richard Verschoor, Theo Pourchaire and Marcus Armstrong, who will take pole for Saturday’s reverse-grid sprint race, rounding off the top 10.
