However the race was overshadowed by an early crash involving Alvaro Bautista and Jorge Lorenzo that forced the world championship leader out of the race and denied him the chance of a fourth successive victory.
Lorenzo was furious after being taken out at turn one and the race direction later launched an investigation into the crash as the Spaniard was forced to watch Stoner join him at the top of the overall standings. An apologetic Bautista said: "I was behind Dovizioso and I tried to go on his side and I missed the break point.
"At the end I arrived so fast into the corner and I tried to stop the bike to stop Lorenzo from dropping out. I'm so sorry for him."
Stoner, for whom this was a second win in Assen following his success here in 2008, admitted that his strategy of tracking Pedrosa and then pouncing paid off as he went on to win by a margin of almost five seconds.
"I didn't see the crash (involving Lorenzo), I was just focused on the front," the 26-year-old Australian told the BBC.
"What a difference a day makes. This morning things weren't looking too good, but the team put a bike under me that was capable of winning. Hats off to the team.
"I decided to follow Dani because I knew we were pulling away from the rest and I needed to save every ounce of energy."
Pedrosa, who moves to within 19 points of Lorenzo and Stoner in the overall standings, was gracious in defeat.
"I think I used a lot of energy in the beginning," said the Spaniard. "I tried to pull away from Casey but he was very close to me all the time.
"He improved his rhythm. Basically I think he saved some energy driving behind. At the end I had some problems changing direction. I was maybe a little bit tired. I think he saw that and took advantage of it."
Dovizioso said that finishing on the podium was an "unbelievable" feeling, while Spies could also be pleased with what was his best performance of the season so far.
And Cal Crutchlow, who broke and dislocated his left ankle at Silverstone two weeks ago, came in fifth.
However, seven riders failed to finish the race despite conditions that were a far cry from the rain that twice interrupted Friday's qualifying session.
It was also a miserable day for Valentino Rossi, with the Italian seven-time world champion ending up at the back of the field after being forced into the pits to get a new rear tyre with ten laps remaining.