Polesitter Marquez was lightning off the start but so was Dovizioso as the two pre-race favourites headed into Turn 1 already locked together, despite Jack Miller (Pramac Racing) heading in slightly hot and almost clipping the number 4 Ducati ahead of him.
But all's well that ends well and this was just the beginning, with the Italian and Spaniard even making slight contact on the run into Turn 3 at 300km/h. Marquez was on the inside and Dovi on the outside, but the number 93 went in hot and ran wide, the Ducati then also forced to sit up. That let Quartararo sweep through to lead, with Miller and Team Suzuki Ecstar's Alex Rins then also pouncing on the exit and Marquez having another wobble as he gassed it to try and slot back into the pack.
Dovizioso was behind Marquez after the shuffle, but he was back past into Turn 4 as Quartararo started putting the hammer down in the lead. The Frenchman was 0.5 ahead onto Lap 2, but Dovizioso and Marquez started to make up ground as they recovered from a frantic opening lap.
Dovi was soon back up to second, with Miller holding off Marquez - for the time being - and fast-starting Valentino Rossi (Monster Energy Yamaha MotoGP) not far off, ‘The Doctor' climbing his way up to fifth from P10 in the opening exchanges and initially in the battle for the podium.
Before long, Marquez had dispatched Miller and the top three started to edge away from the number 43, Rossi and Rins.
Then on Lap 7, Quartararo was under serious attack: Dovizioso blasted past into the lead, before Marquez shot past the Yamaha moments later. The two were back in front, and the duel was just getting started.
Heading into the last corner, the Ducati pulled out from behind the Honda as Dovizioso pulled a Marquez - pushing his machine into the gap and on the verge of creating space rather than using it.
It was roles reversed from 2017 as the Italian lunged down the inside, keeping it perfectly pinned to deny Marquez and power towards the line ahead for his second win of the season. With no chance to strike back, Marquez was forced to settle for second. Behind the duel, Quartararo took the chequered flag in a lonely third to claim his third MotoGP rostrum.