The Ducati rider broke the Algarve’s old lap record with one minute in 38.494 minutes on his final lap, but a 2020 fall of Portuguese poleman Miguel Oliveira brought out the yellow flags and cost Bagnaia his lap.
Aprilia’s Aleix Espargaro set the early benchmark with a solid 1: 39.452, but it was broken by Quartararo, who shot in a weekend best of 1: 39.028.
The FP4 pacesetter was well on the way to improving this on his second lap, but a crack at the front end of his Yamaha while braking for Turn 8 forced him to abandon.
At the same time, Pramac’s Johann Zarco was putting serious pressure on Quartararo’s lap, but he crashed on Turn 11 at Portimao.
This affected both Bagnaia on the Ducati and Quartararo’s team-mate Maverick Vinales, whose fastest laps were canceled at the time.
This left Bagnaia from second to 11th and Vinales from fifth to seventh, with Petronas SRT’s Franco Morbidelli being promoted to second place due to the round’s cancellation.
Quartararo exceeded his previous performance in the first lap of his second run with 1: 38.862 minutes before Bagnaia put him under enormous pressure.
Bagnaia overtook the field by more than four-tenths on his final attempt, only to take it to 11th place when Quartararo made his 11th place.
Suzuki’s Alex Rins jumped from nine to third late, while Bagnaia’s broken lap pushed Rins to second.
Leader Zarco’s earlier fall didn’t hurt his confidence much, as he saved a front row start with 1: 39.991 minutes and put him in third place ahead of Jack Miller and Morbidelli.
Returning six-time MotoGP World Champion Marc Marquez was quickest in Q1 and will start his first race in nine months from the second row in sixth, while Aleix Espargaro leads the third row with the Aprilia.
Luca Marini achieved his best MotoGP qualifying result in eighth on his Avintia Ducati, while World Champion Joan Mir – who followed Marquez through Q1 – was only ninth on the second Suzuki.
Oliveira remained in 10th place after his late fall, with Bagnaia leading Yamaha’s Vinales, who ended up canceling two quick laps to complete the top 12.
Alex Marquez was the only LCR representative in qualifying after teammate Takaaki Nakagami decided to skip the session as he struggled with a shoulder injury from his scary FP2 crash.
The younger Marquez brother was unable to fight for a Q2 spot, finishing in 13th place 0.228 seconds away, while Pol Espargaro was 14th place 0.066 seconds behind.
The preparations of the Honda works driver for Q1 were somewhat disrupted by a heavy high-side in the last corner in FP4, but went largely unscathed.
Brad Binder starts from 15th place on the KTM ahead of Avintia rookie Enea Bastianini, while Valentino Rossi’s problems continue in 2021, as he was only 17th on his SRT Yamaha.
Danilo Petrucci led Tech3 team-mate Iker Lecuona in 18th place, while Lorenzo Savadori at Aprilia was the last of the runners in Q1 in 20th place.
Nakagami’s participation in Sunday’s race seems dubious, while Pramac rookie Jorge Martin has been ruled out after his violent fall in FP3 that took him to the hospital.