Ducati's Marquez held provisional pole with his time of 1 minute 42.481 seconds, but a late scorching 1:42.371 from Martin catapulted the championship leader to the top of the timesheets.
"It's a situation that I'm getting used to, we struggle a bit on Friday, then we do a great job trying to analyse well, and then we make a big step on Saturday," Martin said.
"That was the target. I didn't expect to fight for the pole position. I was aiming maybe for the first row, but I was able to do a great lap, honestly."
Martin leads Marquez by 12 points in the championship and will look to widen that gap in Saturday's sprint and Sunday's race.
For Marquez, qualifying ended in frustration after a few late errors, including an excursion onto the gravel while pushing for a faster time.
"I'm happy, but of course, with that second tyre, too many mistakes. I was just able to push in the last lap, and again, another big mistake," he said.
"Starting in the front row was the main target. Let's see if in the sprint race we can do a good pace."
KTM's Pedro Acosta, who claimed the first MotoGP victory of his career in the Austrian Grand Prix last month, completed the front row.
Japan's Ai Ogura of Trackhouse Racing was 11th-quickest after topping the first qualifying session.
