MotoGP leader Bagnaia takes tumble in third Malaysia practice
It left Ducati's Bagnaia, who was not hurt and can win the world title on Sunday, only 11th fastest at a gloomy Sepang and forced into the first qualifying session.
France's Quartararo was seventh on his Yamaha, 0.484 seconds behind pace-setter Jorge Martin (24) of Spain, who clocked a leading time of one minute and 58.583 seconds on his Prima Pramac machine.
South Africa's Brad Binder (27) went fastest on Friday with one minute 59.479 seconds.
Bagnaia's misfortune came late in the session as he tailgated Quartararo.
The Italian can win his maiden world title on Sunday if he takes the chequered flag and Quartararo finishes outside the podium.
Otherwise the title fight goes to the last race of the season, at Spain's Valencia in a fortnight.
The final Malaysia practice takes place in the afternoon, followed soon after by two qualifying sessions.
The weather could play a crucial factor with rain expected in the late afternoon.