Stoner learnt from his mistake of last year, when he started from pole only to crash on lap six, by letting Honda team-mate Pedrosa move ahead early on and even permitted reigning world champion Lorenzo to lead briefly after the Yamaha rider overtook both Hondas.
Stoner moved ahead on the second lap followed by Pedrosa, who went on to lead from laps seven to 12 before before being reeled in during a battle between the Spaniards and the Australian.
The Australian, who had already won here in 2008 and 2009, thereby claimed the 31st victory of his career.
Reigning Moto2 champion Toni Elias of Spain, who has stepped up to MotoGP this season, had a nightmare race, from his start at the back of the grid to his fall at the end of the race.
Stoner was ecstatic with the brilliant start he's made to life with his new team.
"Testing has all gone well and this weekend we've felt more and more comfortable with the bike and the settings," he told BBC Sport.
"I didn't make the best start and I was a bit worried about people overtaking from behind on the first laps. When I felt comfortable I decided to start moving forward.
"Everything felt good, and as soon as I felt I was able to do a quicker lap than Dani I went for it."
Lorenzo was delighted to have split the Honda duo, saying the result was "maybe the best race of my life."
Pedrosa blamed his decline during the race on injury.
"I was going very good at the beginning but in the middle of the race I had problems with my left arm and couldn't keep control," he said.
"Finally I couldn't use the clutch for shifting as I couldn't hold the grip. I have a problem with this arm and have to fix it somehow."