The Hitech GP driver lined up in fourth but passed Kush Maini for third at the Club chicane on lap four, before swooping past Reece Ushijima for second place at Stowe several laps later.
Championship leader Martins (ART) remained at the front for much of the 17-lap race, having taken the lead off the line from polesitter Ushijima, but Hadjar eventually made it past two laps from the end around the outside of Stowe.
Hadjar had been running fourth in the standings, 15 points adrift of his fellow Frenchman, but the win moves him up to third at the halfway point of the season.
Martins settled for second, while Van Amersfoort Racing's Ushijima rounded off the podium places.
The start was initially aborted after Carlin’s Brad Benavides suffered an issue on the formation lap, with a second formation lap being run prior to the race start. The rookie eventually made his way round to the pits, and rejoined 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 on the first lap into the Club chicane, 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 as the top three bunched up and Martins eventually moved into second at Stowe.
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 with damaged suspension which prompted the safety car.
Racing resumed on lap 13, with Hadjar closing in on Martins for the lead, biding his time and 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.
FIA F3 Silverstone sprint race - results
