The Petronas Yamaha rider dominated the first two races of 2020 but failed to make the podium in the following five races.
Franco Morbidelli maintained his pole position from the start line ahead of Jack Miller’s fast-starting Pramac Ducati.
As the field tightened into the first two turns, Danilo Petrucci had a moment accelerating from Turn 2, forcing Johann Zarco to look to avoid the factory Ducati in front.
But Zarco tucked in the front end of his Avintia GP19 and slid into Dovizioso’s side on sister plant Ducati, knocking them both out of place.
At the front, Valentino Rossi found his way onto Miller at Turn 5 and set about chasing his protege Morbidelli up front.
Miller fell out of form en route at Turn 10, nearly wiping out Rossi while Quartararo capitalized on that to move into third place.
Morbidelli’s lead over Rossi was half a second in the early stages, with the Yamaha trio dropping Miller fairly quickly.
Quartararo moved into the first corner ahead of Rossi at the start of lap six, three laps later he would take the lead from his Petronas teammate at the same spot.
Morbidelli narrowly passed Quartararo, but his hopes of victory were dashed when he nearly crashed twice en route to Turn 1 on Lap 14, dropping to third place behind Rossi.
Rossi was six tenths down on Quartararo but hopes of a 200th MotoGP podium in his 350th premier-class start were dashed when he slipped at Turn 2.
Morbidelli was again promoted to second, but his rear end faded dramatically in the final stages as both Suzukis found their way to push him off the podium.
Jon Mir bounced back from a stable start to finish second ahead of Morbidelli after passing the Petronas rider at Turn 1 on the penultimate lap.
The Suzuki rider extended Quartararo’s lead – which was over three seconds at times – and was just under a second from the checkered flag.
Rins came through from 13th on the grid to push Morbidelli back at Turn 10 on the same lap and followed Mir home for his first podium of the season and the first double podium for Suzuki since Misano in 2007.
Morbidelli stayed just 0.545s ahead of the Pramac duo of Miller and Francesco Bagnaia in fourth, closely followed by Takaaki Nakagami in seventh on the LCR-Honda.
Petrucci finished eighth with his factory team Ducati, while Maverick Vinales finished a close ninth on his Yamaha after a miserable afternoon.
Vinales got off to a poor start from fifth on the grid and found himself out of the points in 16th at the end of the first lap. On the M1 he struggled to overtake and benefited greatly from falls ahead.
The Yamaha rider beat LCR’s Cal Crutchlow in the closing stages in 10th place, with points rounded out by KTM’s Brad Binder, Aprilia’s Aleix Espargaro, Alex Marquez’s Honda, Iker Lecuona (Tech 3) and Avintia’s Tito Rabat.
Pol Espargaro on the KTM crashed out of contention for the top six on lap 13 and was later joined on the sidelines by Tech 3’s Miguel Oliveira.
Quartararo’s third win of 2020 now puts him eight points clear in the championship, while Mir moves up to second with his fourth podium of the year.
Vinale’s nightmare means he falls 18 points behind while Dovizioso is 24 points in fourth place. Now, 50 points adrift, Rossi’s hopes have taken a heavy hammer blow.