Vinales takes Yamaha's first victory of the season at the Dutch MotoGP, after edging clear of Marquez in the closing stages at Assen.
Rookie star Quartararo, starting from back-to-back poles, spent large parts of the race in the lead but had to shut the throttle during some scary highspeed-wobbles down the back straight.
The Frenchman, still recovering from arm pump surgery, eventually settled into third for his second rostrum in a row.
Vinales and Quartararo chose the hard rear tyre, with Marquez - who extends his title lead over Dovizioso - on the soft.
Rins took the holeshot from Suzuki team-mate Mir, only to fall from the lead on lap 3.
Rossi - who had qualified down in 14th - was also out early after tangling with Nakagami, the Japanese needing medical assistance after their fast Turn 8 incident, but later described as 'okay'.
Jorge Lorenzo was ruled out of the remainder of the Assen event, and next weekend's German round, after suffering fractures to his vertebrae during FP1 on Friday.
| Dutch MotoGP - Race Results | ||||
| Pos | Rider | Nat | Team | Time/Diff |
| 1 | Maverick Viñales | SPA | Monster Yamaha (YZR-M1) | 40m 55.415s |
| 2 | Marc Marquez | SPA | Repsol Honda (RC213V) | +4.854s |
| 3 | Fabio Quartararo | FRA | Petronas Yamaha (YZR-M1)* | +9.738s |
| 4 | Andrea Dovizioso | ITA | Mission Winnow Ducati (GP19) | +14.147s |
| 5 | Franco Morbidelli | ITA | Petronas Yamaha (YZR-M1) | +14.467s |
| 6 | Danilo Petrucci | ITA | Mission Winnow Ducati (GP19) | +14.794s |
| 7 | Cal Crutchlow | GBR | LCR Honda (RC213V) | +18.361s |
| 8 | Joan Mir | SPA | Suzuki Ecstar (GSX-RR)* | +24.268s |
| 9 | Jack Miller | AUS | Pramac Ducati (GP19) | +26.496s |
| 10 | Andrea Iannone | ITA | Factory Aprilia Gresini (RS-GP) | +26.997s |
| 11 | Pol Espargaro | SPA | Red Bull KTM Factory (RC16) | +28.732s |
| 12 | Aleix Espargaro | SPA | Factory Aprilia Gresini (RS-GP) | +34.095s |
| 13 | Miguel Oliveira | POR | Red Bull KTM Tech3 (RC16)* | +34.181s |
| 14 | Francesco Bagnaia | ITA | Pramac Ducati (GP18)* | +34.249s |
| 15 | Hafizh Syahrin | MAL | Red Bull KTM Tech3 (RC16) | +34.494s |
| 16 | Tito Rabat | SPA | Reale Avintia Ducati (GP18) | +48.357s |
| 17 | Karel Abraham | CZE | Reale Avintia Ducati (GP18) | +1 lap |
| Johann Zarco | FRA | Red Bull KTM Factory (RC16) | DNF | |
| Takaaki Nakagami | JPN | LCR Honda (RC213V) | DNF | |
| Valentino Rossi | ITA | Monster Yamaha (YZR-M1) | DNF | |
| Alex Rins | SPA | Suzuki Ecstar (GSX-RR) | DNF | |
* Rookie.
