The reigning world title-holder burst out front with 1min 30.088secs, 0.011 ahead of Rossi's 1:30.099 as Andrea Dovizioso rounded out the top three.
Marquez holds a comfortable 72-point lead over Dovizioso heading into Sunday's race, where he is looking to close in on his fifth world title.
But Jorge Lorenzo, who arrived carrying a foot injury and then damaged his wrist in a heavy crash during practice, will miss the race after he pulled out before qualifying.
Thailand's first MotoGP is being held in the town of Buriram, which is several hours' drive from Bangkok and has a population of only about 30,000.