A see-saw battle saw the the lead change hands numerous times before the 36-year-old Rossi opened up a slight gap on the final two laps and held off the charging Dovizioso on his Ducati, who was looking for his first win in MotoGP.
Spaniard Jorge Lorenzo, also on a Yamaha, was also in the hunt for victory and led midway through the race before Rossi, who began from eighth on the grid, charged to the front and went into battle with his compatriot Dovizioso.
World champion Marc Marquez never fully recovered from a dreadful start when he was forced off the track and left last, although the Spaniard did battle back to finish fifth.