Dovizioso's fellow Italian teammate Danilo Petrucci was third while veteran superstar Valentino Rossi of Yamaha won plaudits for racing in pain from a training accident and finishing fourth having set the early pace.
Rossi had gone into the race looking worried and drawn.
"I couldn't really ride the way I would have liked to," he said. "I will try to recover and be in perfect shape in Barcelona (next weekend)," a deeply disappointed Rossi said.
The four had opened an ominous gap on the rest of the field hitting top speeds of 340kph (211mph) on the long straight and Vinales, on a Yamaha, set much of the pace having won three races so far this season.
