Desperate to stand on the podium in front of his home fans after such a tough season, and bolster his hopes of staying at Ducati, Hayden made his patriot-liveried Desmosedici as wide as possible and held off Dovi by 0.5sec at the flag.
While Hayden celebrated in prac ferme, countryman Edwards slumped into his chair at the Tech 3 pits clearly underwhelmed by his fifth place finish.
Team-mate James Toseland was more content, having once again matched his career best result of sixth. The Englishman battled Marco Melandri for much of the race, until the Hayate rider crashed with just three laps to go.
Loris Capirossi claimed seventh for Suzuki despite finishing the first lap down in 14th, while Mika Kallio finished his second race as a factory Ducati rider in eighth - equalling the best result of his rookie season to date.
de Angelis' team-mate Toni Elias ran onto the grass through the opening corners before climbing back up to ninth, while the recovering Pedrosa snatched tenth from Chris Vermeulen (Suzuki) at the line.
Aleix Espargaro became the youngest ever Spanish rider to start a MotoGP race at the age of 20 years and 31 days on Sunday. Espargaro, whose youngest brother Pol won the 125cc race, had been impressive in practice and qualifying but ran onto the grass with Elias on the exit of turn one before riding to 13th place for Pramac Ducati.
The first race to be held at Indianapolis Motor Speedway was a motorcycle race, in 1909.
Round 13 of the 2009 MotoGP World Championship will be held at Misano next weekend, Rossi's home race.
Indianapolis Grand Prix:
2. de Angelis
12. de Puniet