The Australian, son of MotoGP great Mick Doohan, started in fourth and passed championship leader Hauger on lap 14.
There was less than a second between the pair in the charge to the finish, but Red Bull Junior Doohan emerged victorious, finishing 1.5s in front to take his second podium in the series.
MP Motorsport’s Caio Collet finished third to take his second podium of the year, beating teammate and Alpine Academy driver Victor Martins to third, despite the latter having started there.
Trident’s Clement Novalak finished fifth, with polesitter Frederik Vesti (ART Grand Prix) ending up in sixth.
Hitech Grand Prix’s Ayuma Iwasa finished in seventh, with ART Grand Prix’s Alexander Smolyar, who won Saturday’s first sprint race, rounding off the points finishes.
Hauger took the lead off the line from Vesti amid a lot of spray, with rain having fallen on Sunday morning.
Novalak took third on the second lap, but eventually…