The Hitech driver lined up in fourth, but passed Kush Maini for third at Vale on lap four, before swooping past Reece Ushijima for second place at Stowe several laps later.
Championship leader Martins (ART) managed to hold his position for much of the 17-lap race, having taken the lead off the line, but Hadjar eventually made it past two laps from the end around the outside of Stowe.
Hadjar had been running in fourth in the standings, 15 points adrift of his fellow Frenchman, but the win will move him up to third at the halfway mark of the season.
Martins settled for second, while Ushijima, who started on pole for Van Amersfoort Racing, rounded off the podium places.
The start was initially aborted after Carlin’s Brad Benavides suffered an issue off the line, prompting a second formation lap before the race start. The rookie then pitted, eventually making his way out at the back of the pack six laps down.
Martins took the lead into Abbey off the line, while Ushijima and Maini tussled for second.
Further back, Prema Racing’s Ollie Bearman lost two places in the first lap into Vale, with Maloney taking seventh place.
Jonny Edgar, making his return for Carlin after taking an illness-enforced break from racing, also dropped two places to David Vidales and Franco Colapinto to run in 15th.
Hadjar moved up to third on lap four, while the following lap, Ushijima was running within 0.5s of Martins out front, bunching up the top three.
The safety car was deployed on lap 10 after Charouz Racing System team-mates Laszlo Toth and Zdenek Chovanec collided at Club, with the latter attempting to move down the inside before hitting Toth’s rear right tyre.
Chovanec, who returns to F3 this weekend in place of Lirim Zendeli, was unable to get going again and prompted the safety car.
Racing resumed on lap 13, with Hadjar closing in on Martins for the lead, biding his time before eventually taking the lead around the outside of Stowe on the penultimate lap.
Maini took fourth, with Hitech’s Kaylen Frederik in fifth and Roman Stanek, currently second in the standings, in sixth for Trident.
Maloney finished seventh, with the Prema trio of Arthur Leclerc, Bearman and Jak Crawford rounding off the top 10.
Result:
