Quartararo took the lead on the fifth of 20 laps, pulling away from the rest of the field to create a 65-point deficit in the championship on reigning world champion Joan Mir, who finished ninth in the race.
Honda’s Pol Espargaro turned his first pole for the Japanese brand into the holeshot at the start, followed by Quartararo and Aleix Espargaro at Aprilia.
After a sluggish start, Francesco Bagnaia tossed his Ducati inside Quartararo and Aleix Espargaro to briefly finish second while drama unfolded behind them.
After a near miss in Stowe between Pramacs Jorge Martin and Marc Marquez, the Honda rider contacted Martin in the club corner and took them both out of the race.
Aleix Espargaro finished second at Bagnaia in Brooklands at the end of the first lap and made it an Espargaro 1-2 as the leaders roared on the second tour.
The top four of Pol and Aleix Espargaro, Bagnaia and Quartararo were already six tenths behind in the second round.
Quartararo demoted Bagnaia on the following tour before soon overtaking Aleix Espargaro to lead the chase on the Honda-mounted Pol Espargaro.
On lap five, Quartararo tore the inside of Pol Espargaro at the fast left bend of the farm to take the lead.
Aleix Espargaro beat Pol on lap six at the Vale, but Quartararo lost the lead and would quickly find a lead of over three seconds.
Able to manage his tires at the front of the field, Quartararo won his fifth win in a 2021 season that he is quickly taking control of.
Suzuki’s Alex Rins had worked his way up to second place just above the middle distance and staged his race from then on to hold onto second place for his first podium in 2021.
Jack Miller stormed the podium late with his factory Ducati and made Aleix Espargaro even stronger in the closing stages.
The Australian started a raid on the third in the Village corner on the final lap, but Espargaro pulled out and cut back under Miller on the loop to regain position.
Espargaro drove a defensive line through Brooklands and Club, fending off Miller by 0.149 seconds, securing Aprilia’s first podium in the modern MotoGP era – and Espargaro’s first premier class podium since Aragon 2014.
Pol Espargaro completed the top five for his best result of his first Honda season, with Brad Binder finishing sixth on the factory KTM.
Iker Lecuona followed Binder home in seventh place on the Tech 3 KTM, securing his best ever dry MotoGP result, while Alex Marquez (LCR Honda) led Mir and Danilo Petrucci’s second Tech 3 KTM.
Johann Zarco had a difficult afternoon on the Pramac Ducati when Avintias Enea Bastianini and LCRs Takaaki brought Nakagami Bagnaia back to a mysterious 14th place.
The last point went to the second Avintia Ducati from Luca Marini, while Miguel Oliveira from KTM, Cal Crutchlow from Yamaha and the Petronas SRT duo Valentino Rossi and Jake Dixon rounded off the 19 ranked finishers.