"Assen is one of the tracks I like more on the calendar," said Vinales, whose last win was in Australia last October. "Right now I am living my dream because it's been such a long period without victory."
Marquez now has 160 points to 116 for Italian Andrea Dovizioso, who finished fourth for Ducati, after eight of 19 races won by four manufacturers.
"We knew that the Yamaha was very strong already in practice," said Marquez, who recognised Vinales was faster but stuck with him as long as he could before easing off.
"This is like a victory. We increased the advantage of the championship, this is the most important. And in a circuit where we struggle, we were there."
Italian great Valentino Rossi, Vinales's team mate, crashed out after four laps after tangling with Japanese rider Takaaki Nakagami. Neither were injured.
"It was my mistake. It was also a quite big crash," said Rossi.
Suzuki riders Alex Rins and Joan Mir led into the first corner, with Vinales also ahead of Quartararo, who had arm surgery at the beginning of June and was not helped by his bike's handling.
Rins slid out on lap three with Mir leading until Quartararo again hit the front with Marquez between the two Yamaha team riders.
Vinales took the lead with 11 laps to go with the two Spaniards close together before the Yamaha rider pulled clear to win by 4.8 seconds.
The next race is the German Grand Prix at the Sachsenring on July 7.
(Reporting by Alan Baldwin, editing by Clare Fallon and Pritha Sarkar)
