Rookie Virtuosi started fourth, before edging out Juri Vips, Jehan Daruvala and Enzo Fittipaldi to take the lead on lap eight after the Charouz driver went wide at Village.
Doohan pulled a nearly five-second gap on lap 16 before Iwasa launched his fightback, setting the fastest laps in his bid to take the lead from DAMS.
But the Aussie held on to take the checkered flag and bring the Doohan name back to the top step of a British Grand Prix weekend for the first time since 1997, when his father Mick won the British 500cc Motorcycle Grand Prix at Donington.
Despite closing the gap to the Australian by nearly five seconds to 0.9 seconds on the line, Iwasa settled for second place, having started fifth, with Fittipaldi completing the podium.
The race started behind the safety car, with wet conditions causing disruption throughout the day.
Much of the early laps were processional, with just one move when Jake Hughes passed Dennis Hauger for 12th, before the move was called off a lap later.
Fittipaldi took the lead from Daruvala on the pit straight on lap six, before the Prema driver was also passed by Doohan. Further on, Iwasa passed Vips for fifth place as the Hitech rider began to drop down the order.
Doohan took the lead from Fittipaldi two laps later, with Iwasa moving up to third before passing Fittipaldi at Copse.
Theo Pourchaire passed Daruvala at Copse on lap 10, while Vips’ bad luck continued as he was handed a five-second penalty for going over the track limits.
Ayumu Iwasa, Dams
Photo by: Red Bull Content Pool
Doohan was five seconds ahead on lap 16, setting consecutive fastest laps, with Daruvala falling prey to championship leader Felipe Drugovich for fifth at Stowe.
Iwasa set the fastest lap two laps later, closing the gap to the leader to 3.5 seconds, then to 2.5 seconds on the penultimate lap.
But Doohan held on to claim his first F2 victory, having last climbed to the top step of the podium at Sochi in FIA Formula 3 last season.
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Pourchaire took fourth, Drugovich fifth and Frederik Vesti sixth after an intense battle on lap 18 between ART driver Logan Sargeant (Carlin) and Daruvala.
Marcus Armstrong finished ninth, with his Hitech teammate Vips rounding out the top 10.
FIA F2 Great Britain: Full sprint race results