Quartararo repeated his route to victory in Doha, Algarve, recovering from sixth place at the end of the first round to take an early lead and dominate to gain a 15-point lead in the championship.
Johann Zacro put his Pramac Ducati in the lead at the start as policeman Quartararo dropped to sixth place while Marquez jumped to third place.
Marquez was downgraded from third place by reigning world champion Joan Mir, the Suzuki rider who made an aggressive move against the Honda at the Portimao right-handed man.
The pair hit again at Turn 3 on the following lap when Marquez hit the rear of Mirs Suzuki and was lucky enough to remain mounted. Quartararo used it to move back up to fourth place.
IIn the main battle, Zarco held on, but came under heavy pressure from the Suzuki of Rins, who made a pass-stick on lap 13 at turn 13 – although Zarco came back a moment later on the main straight.
Rins played another game for the lead at turn 13 at the end of lap five, while Quartararo beat Zarco at the next corner.
The Suzuki rider took the lead for the next two laps, and Quartararo dragged himself into Turn 1 on the ninth tour through Rins.
The pace for Quartararo and Rins was hot. The couple drove the fastest laps several times and was able to close a gap of more than a second compared to the fighting Zarco and Mir behind them.
Rins kept the pressure on Quartararo but the Frenchman didn’t crack and kept his lead.
Quartararo’s afternoon was relieved seven laps after the end when Rins pushed too hard in his chase and crashed at Turn 5, giving the Yamaha rider well over four seconds ahead of the remaining tours.
Rins’ fall put Zarco in second place while Ducati’s Francesco Bagnaia found a way through Mir.
However, Zarco’s podium was finished on lap 20 when he crashed at Turn 10. The battle for second place was between Bagnaia, Mir and Franco Morbidelli from Petronas SRT.
Quartararo was not threatened by the checkered flag to secure his second straight win in 2021.
Bagnaia struggled against Mir and took second place with his Ducati, while Morbidelli was fourth from 15th on the grid, ahead of Brad Binder of KTM.
Aleix Espargarao was a factor in the podium early on, but the Aprilia rider finished sixth and got his best result at the RS-GP.
Marc Marquez’s last MotoGP race before Sunday’s Portuguese GP ended in a potentially career-threatening crash.
But he put those demons in seventh place in the Algarve, the six-time MotoGP world champion who led home his LCR Honda-mounted brother Alex Marquez, Avintia rookie Enea Bastianini and injured Takaaki Nakagami (LCR).
Maverick Vinales suffered a mysterious loss of form at the end of the first lap on his Yamaha, the Qatar GP winner, and was only able to save 11th place after a series of falls.
He ran Luca Marini (Avintia), Danilo Petrucci from Tech 3, Lorenzo Savadori from Aprilia and the sister tech bike from Iker Lecuona, while last year’s Portuguese race winner Miguel Oliveira finished 16th after a crash.
Valentino Rossi crashed from eleventh in the closing stages and the SRT rider joined Ducati’s Jack Miller after an early crash.
Pol Espargaro retired at the end of lap five due to a technical problem with his Honda.