With Hayden having dropped to twelfth after a detour through the gravel, the closing stages saw Dovizioso and Simoncelli - who had rejoined in ninth and eleventh after their penalties - fighting for fourth place.
Gresini rider Simoncelli got the better of the yet-to-sign Dovizioso at the end of the 22nd lap, while Ben Spies - battling food poisoning this weekend - recovered from a distant last all the way to sixth place, just ahead of Hayden.
Another American, Colin Edwards, claimed eighth for Monster Yamaha Tech 3, with home hero Hiroshi Aoyama ninth for Gresini and Randy de Puniet
tenth for Pramac Ducati.
Crutchlow finished eleventh, with Honda wild-cards Kousuke Akiyoshi and Shinichi Ito the last of the finishers in twelfth and 13th.
Australian Damian Cudlin, making his MotoGP debut as a replacement for the injured Loris Capirossi
at Pramac Ducati, crashed out of 14th - while just behind Akiyoshi - on lap 15. An unfortunate end to an otherwise impressive weekend.
Aspar Ducati's Hector Barbera was the only rider not to walk away from an accident, the Spaniard being carried off on a stretcher after his lap 2 incident.
MotoGP rookie Karel Abraham (Cardion AB) withdrew from the race due to concentration problems caused by the head impact he suffered at Aragon on September 18.
Stoner will start his home Australian Grand Prix, at Phillip Island on October 16, with a 40-point lead over Lorenzo, with 75 points remaining.
Japanese Grand Prix:
10. de Puniet