The Prema rookie lined up second before passing poleman and championship leader Theo Pourchaire (ART) at Turn 3.
Ferrari junior Bearman endured five safety cars, with a quick pitstop allowing him to emerge just ahead of Pourchaire to secure him victory.
Ayumu Iwasa finished second for DAMS, having passed the Frenchman on lap 27, with Pourchaire third as the race finished behind the safety car.
Vesti crashed out on lap one after contact from Roman Stanek (Trident) leaving him point-less and handing Pourchaire a 25-point lead heading into the season finale at Abu Dhabi.
Poleman Pourchaire held the lead off the line, but was passed by Bearman at Turn 3, before Vesti spun out at Turn 5 after being nudged onto the grass, prompting the first safety car, as Clement Novalak (Trident) also crashed after contact from Amaury Cordeel (Virtuosi).
Racing resumed on lap four but the safety car was deployed again three laps later, with Arthur Leclerc (DAMS) crashing down the Turn 1 escape road, ending his race.
Most of the field stopped under the safety car, with Jehan Daruvala (MP Motorsport) inheriting the lead ahead of Jack Doohan (Virtuosi) and DAMS driver Iwasa, who had benefitted from the chaos to make up 12 places.
Bearman was perilously close to Pourchaire in the pits, but edged out ahead, with no further action after an investigation for unsafe release, to hold position.
Though the safety car pulled into the pits ahead of lap 12, it was almost immediately redeployed after Zane Maloney (Rodin Carlin) was hit from behind by Roy Nissany at the restart, causing a wreck on the start-finish straight.
Source: Autosport