Quartararo’s points lead was 10 points before this round, but his worst result of the season and a third for Mir mean he is now six points behind the Spaniard and 15 points covering the first four points.
Franco Morbidelli took the holeshot into the first corner of the line, but the Petronas SRT rider ran far, letting Maverick Vinales and Quartararo through.
Vinales used the early grip advantage of its soft front tire to bring seven tenths of a daylight between itself and Quartararo, while Rins had jumped from 10th to 4th.
Quartararo withstood an attack by his team-mate Morbidelli at Turn 12 on the first lap, but his pace quickly slowed and Rins soon found a way through.
The lead narrowed slightly to half a second, but Rins’ attack continued and he took advantage of the capital as the Frenchman ran wide on the final corner at the end of lap five to finish second.
Quartararo repeatedly ran far in the last two corners and his pace deteriorated considerably over the next 10 tours. The Petronas driver fell out of the points on lap 15 in 17th place.
Rins took the lead from Vinales on lap eight in the final corner and the Yamaha rider fell into the hands of Mir’s sister Suzuki after a brief argument five tours later.
The lead for Rins was 1.1 seconds, but Mir was able to close the gap with Marquez in tow after the Honda rider snuck through from 11th on the grid.
Rins’ advantage dipped to just over six tenths on lap 15, but Mir’s winning challenge would be for nothing and he was powerless to stop Marquez from getting through on lap 18.
Marquez, who made his debut podium in the wet Le Mans race last week, said on Saturday the podium was not a “real goal”.
But when he was away from Me, he quickly got on Rins’ cock and took the pressure off. Despite a massive moment, he regrouped immediately when he accelerated at the last corner of the 21st Tour.
Rins made no mistake on the final lap and had enough in hand to beat Marquez on the checkered flag by 0.263 seconds and become the eighth winner in 2020.
Mir’s pace dropped on the final lap, but not enough to get Vinales back on the podium. For the first time, the Suzuki driver led the overall standings with six points.
After fourth place, Vinales is only 12 points away from the championship lead. Takaaki Nakagami completes the top 5 of his LCR Honda ahead of Morbidelli.
Andrea Dovizioso recovered from 13th place on the grid to seventh place. Quartararo’s misery meant the Ducati rider is only 15 points away from the championship lead.
Cal Crutchlow on the sister LCR bike followed Dovizioso home from third place after a shocking start. Pramac’s Jack Miller led Avintia’s Johann Zarco to round out the top 10.
The KTMs were led by Brad Binder in 11th ahead of Pol Espargaro, with Aleix Espargaro on Aprilia, Iker Lecuona from Tech 3 and Danilo Petrucci (Ducati) taking the final points.
Quartararo couldn’t get more than 18th place on the checkered flag, only Bradley Smith on the Aprilia and Avintias Tito Rabat behind him after Francesco Bagnaia (Pramac) fell early.