The evergreen 38-year-old claimed his first victory for a year and his 10th at Assen after a thrilling duel with compatriot Danilo Petrucci.
Rossi nabbed the win by barely the length of his Yamaha bike from Petrucci, with defending champion Marc Marquez taking third.
Dovizioso finished fifth to take the championship lead from Maverick Vinales, who crashed out.