The Williams junior led from the off, holding off challenges from ART team-mates Frederik Vesti and Theo Pourchaire to take his first win since Sochi in FIA Formula 3 last year.
With Vesti falling away during the first lap, Sargeant held on through a safety car, building up a gap of 1.5s to Pourchaire by lap seven.
The pair both pitted four laps later, emerging in the same order as championship leader Felipe Drugovich took the lead on track.
As those in front pitted, the leading pair continued to tussle for the top spot, with Pourchaire just 0.5s behind by lap 26.
But Sargeant rebuilt the gap to his rival and crossed the line 1.5s ahead to become the first American F2 race winner.
Carlin’s Liam Lawson completed the podium, having started fifth before taking advantage of poor starts from Vesti and Drugovich to secure his fifth podium of the season.
Drugovich and Vesti lost two places apiece on the first lap before the safety car was deployed after contact between Roy Nissany and Dennis Hauger.
The DAMS driver went wide towards the end of the Wellington Straight, coming back on track and making contact with the reigning FIA Formula 3 champion.
Hauger was then forced off across the grass at Brooklands and flew over the sausage kerbs, coming back on track and landing on Nissany’s car as they both piled into the gravel.
A scary shunt in #F2 this morning, Dennis Hauger's car launched over a sausage kerb and t-boned Roy Nissany's car!
