Goalkeeper Eisa delivered a fantastic performance against Al Hilal to help Al Ain reach the final
The 20-year-old Frenchman sealed pole with a 1min 29.719sec qualifying lap, just ahead of Spanish compatriots Maverick Vinales and Marquez.
Quartararo's rookie season has seen the Petronas Yamaha rider climb to seventh in the rankings, fast emerging as one of Marquez's biggest rivals.
"I'm really looking forward to tomorrow's race," a beaming Quartararo told MotoGP TV.
Marquez, 26, has a comfortable 98-point lead against his closest rival Ducati's Andrea Dovizioso, who finished seventh in qualifying.
The Honda rider only needs to best Dovizioso by two points in Sunday's race to seal his sixth premier class title and eighth overall championship.
But he has struggled throughout in Buriram, with a crash sending him to hospital on Friday and another spill during qualifying.
Marquez later told reporters he was still happy with the result and that he was approaching the race like any other despite the championship looming.
Discussing his physical condition he said he had woken up in pain but that once he started his day there was "not any problem".
He said Friday that the crash left him unable to breath for several seconds.
The superstar won the first Grand Prix in Thailand last year in a thrilling last-corner showdown with Dovizioso.
Clear skies prevailed for the afternoon session after a seasonal downpour soaked the track early Saturday, delaying start times and creating challenging conditions for riders.
The race is being hosted for the second year in a row in the small northeastern town of Buriram, which has boomed on the back of multi-million-dollar investment in sports infrastructure.
But it is scheduled towards the tail end of monsoon season, and more rain is forecast for Sunday's race day.
Goalkeeper Eisa delivered a fantastic performance against Al Hilal to help Al Ain reach the final
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