The 32-year-old also gave Aprilia a maiden triumph in the sport's premier class while he took over the lead of the world championship after three rounds.
Six-time world champion Marc Marquez is out of Sunday's Indonesian Grand Prix after a horror crash in the final morning warm-up.
"This past Saturday, Marc Marquez, while preparing for the Algarve Grand Prix with one of his standard off-road training sessions, suffered a fall that caused a slight head concussion," said Honda's statement.
Quartararo's win comes in his third season in MotoGP, the first with Yamaha's factory team after two years with the SRT satellite outfit. Of the 16 MotoGPs he has contested this season, he has claimed 10 podiums, including five victories.
Rossi announced in August that he would retire after the season-ending race at Valencia on 14 November.
On a track still wet following rain in the morning and at the start of the afternoon session, Australian Miller set a time of 1 min 41.305 on his factory Ducati.
Finland and Indonesia had been due to return to the world circuit in 2020, but their inclusions were also victim to the global pandemic.
Marquez, starting third on the grid, seized the lead at the start and relentlessly powered to victory over championship leader Fabio Quartararo of France.
The Italian, who celebrated his debut win in the premier category last weekend in Aragon, came under intense pressure from championship leader Fabio Quartararo in the closing laps.
Ducati rider Bagnaia, who won his first GP at Aragon last weekend, posted a blistering best time of one minute, 31.065 seconds at Misano, finishing ahead of teammate Jack Miller and championship leader Fabio Quartararo.
The 22-year-old French Yamaha rider hurt his left ankle when he slipped at turn eight at Silverstone.
After the Dutch GP at the end of June, it was announced that Maverick Vinales, who has already signed to ride for Aprilia next season, would cut short his contract and leave at the end of the season.
MotoGP 2021: Malaysian MotoGP called off due to COVID-19 restrictions, Misano circuit to replace race in calendar
"The ongoing Covid-19 pandemic and the resulting entry restrictions for Malaysia oblige the cancellation of the event," a joint statement from the sport's ruling body the FIM and promoters Dorna confirmed.
Unlike his rivals who pitted to change bikes, Binder opted to stay out on slick tyres and skillfully held off the field to win his second-ever MotoGP.
On the fastest track in MotoGP, championship leader Fabio Quartararo seemed to have sealed pole position when he smashed the record set last week by fellow Frenchman Johann Zarco last weekend ahead of the Styria Grand Prix.
French championship leader Fabio Quartararo of Yamaha was third in a race that had to be restarted after the KTM of Spaniard Dani Pedrosa and the Aprilia of Italian Lorenzo Savadori caught fire in the middle of the track following a crash.
Rossi told a press conference ahead of this weekend's Styrian Grand Prix that he will call it a day, 12 years on from his last MotoGP title.
The race was scheduled for 17 October at the Buriram International Circuit.
Organisers planned to stage the races in October and November, but have hit roadblocks over Australia's requirement for overseas arrivals to undergo 14 days of mandatory quarantine.
MotoGP 2021: Maverick Vinales claims pole position at Dutch MotoGP, Marc Marquez to begin in 20th position
Vinales' French teammate and championship leader Fabio Quartararo was second, at 0.071sec, with Ducati's Italian rider Francesco Bagnaia in third (+0.302).