Pedrosa then dropped away when the rain intensified while Dovizioso later backed off to finish his Honda career with a seventh podium of the year.
Fourth place and victory in the Rookie of the Year contest was hotly contested between Cal Crutchlow and Karel Abraham. Fifth and sixth for most of the race, the pair passed Pedrosa on the last lap .
Monster Yamaha Tech 3 rider Crutchlow then sealed his best MotoGP finish and the rookie title by overtaking Abraham, with the Czech rider clipping Crutchlow's rear wheel and running off soon after. Abraham crossed the line eighth.
The incident promoted Pedrosa to fifth, while stand-in riders Katsuyuki Nakasuga (Yamaha) and Josh Hayes (Tech 3) claimed sixth and seventh on their MotoGP race debuts!
Loris Capirossi, making his 328th and last Grand Prix start, rode from twelfth on the grid to ninth, having lost two places in the last two laps. The Italian raced with the #58 on his Pramac Ducati as a tribute to Marco Simoncelli.
Toni Elias also lost ground to finish tenth for LCR Honda, with Hector Barbera (Aspar) and Hiroshi Aoyama (Gresini Honda) the final riders to reach the finish.
All three were making their last appearances for their present teams. Elias' is yet to sign, but Barbera looks set to switch to Pramac and Aoyama is confirmed as riding in World Superbike next season.
A special tribute to Aoyama's team-mate Simoncelli was held at Valencia this morning.
Testing with next year's 1000cc bikes will take place at Valencia on Tuesday and Wednesday.
Valencia Grand Prix: