The Virtuosi driver led from pole for the duration, breaking DRS to Frederik Vesti (Prema) by lap seven before building a five-second lead before Vesti pitted.
Doohan followed suit two laps later and emerged in front, eventually building a nine-second lead for his first win since Belgium last year.
It comes after a struggle so far in 2023, his second F2 season, having only taken two podiums after a strong showing in his rookie year.
Championship leader Vesti finished second to extend his lead to 11 points, fending off a late challenge from Victor Martins (ART), who took his seventh podium amid a stunning rookie season.
There was action from the off as Vesti and Martins tussled at Turn 1, the more experienced driver emerging ahead behind Doohan.
The yellow flags were waved briefly on lap three as Clement Novalak came to a stop on track at Turn 4 in his Trident-run car, but action was not disrupted.
Doohan had broken DRS to Vesti by lap seven as the pitstops started behind, with Zane Maloney the first to swap to the medium tyres for Rodin Carlin.
Ayumu Iwasa, who ran the alternate strategy for DAMS, was quicker than the leaders by this point, running 0.039s quicker than Doohan on lap eight.
Vesti was closing on Doohan by lap 10, with the gap at 0.7s, but it was back up to 1.2s two laps later as Isack Hadjar (Hitech) became the first of the top five to stop.
Theo Pourchaire, running fourth for ART, stopped on lap 13, hoping for a late podium charge, but was stuck behind Virtuosi’s Amaury Cordeel after emerging in 13th, costing him valuable time.
Vesti’s engineers told him he “probably needs to box” on lap 17, but it was five more laps before he finally switched to the medium compound, emerging in fourth, with Martins following suit next time around.
Doohan had stayed out while his rivals emerged, with Martins then embroiled in a fight with his team-mate. Pourchaire ran wide at Turn 2, collecting rubber on his fresh tyres and losing time to Martins who powered ahead, while Pourchaire fell behind Hadjar into sixth.
Doohan finally stopped on lap 24, retaining his lead ahead of Vesti, with Martins in third.
Iwasa soon made it past Pourchaire, having taken an early stop for the soft tyres as degradation was lower than expected, before passing Hadjar on lap 35 up the inside of Turn 1 to secure fourth.
Hadjar finished fifth, with Pourchaire in sixth in a blow to his title fight with Vesti.
Dennis Hauger was seventh for MP Motorsport, with Enzo Fittipaldi (Hitech) eighth, VAR driver Juan Manuel Correa in ninth and team-mate Richard Verschoor rounding off the top 10.
F2 returns next weekend in Belgium with two rounds remaining.
F2 Hungary - Feature race results
