The Prema driver headed team-mate Frederik Vesti in a Safety Car finish, with Jak Crawford rounding out the top three.
The 21-lap encounter twice saw the Safety Car deployed, the second for a multi-car pile-up at the opening corner that accounted for six cars.
That included the then-race leader Dennis Hauger, second-placed Victor Martins, Jehan Daruvala, Theo Pourchaire, Arthur Leclerc, and Jack Doohan, who locked his brakes and spun on approach to the corner.
All struck trouble following a Safety Car restart following Roy Nissany crashing out at Turn 15.
As the field approached Turn 1 at the restart, grip was at a premium.
Hauger went in too hot and grabbed the barrier, spinning him out of the race and promoting Vesti into the lead.
Martins nosed into the barrier, with Daruvala following him in, his car diving under the ART entry, which was left atop the MP Motorsport car.
Pourchaire and Leclerc ran deep and nosed into the barrier earlier in the corner, while Doohan suffered a blocked brake and spun through the pack before losing the engine.
The Safety Car was deployed, but not before Bearman, who'd charged through the field from eighth, could steal away the race lead.
Before the late chaos, Hauger had sprung clear of the pack at the race start with Martins hanging on.
At the race start, Richard Verschoor got loose exiting Turn 1, slewing across the track on the opening lap to open the door for Zane Maloney.
However, the Red Bull-backed driver had contact with Martins off the line, which led to a puncture midway around the opening lap.
That dropped him down the order, promoting Hauger to the lead.
For a time, Daruvala battled Vesti before finally losing out to the Mercedes junior courtesy of DRS, with Bearman working his way by soon after.
Verschoor retired on the opening lap owing to the damage to his car, while Maloney limped back to the pits, where his day ended too.
Ayumu Iwasa was also a retirement after a problem with the DRS flap on his car saw it jam open.
Through it all, Bearman enjoyed strong pace to claim his first Formula 2 race win.
He will also start from pole position for Sunday's Feature race after being the fastest qualifier on Friday.