Marquez made a scorching start and held the inside line on the first turn of the opening lap to surge past Martin, who had set a lap record at the Motegi circuit earlier on Saturday to grab pole position.
Reigning champion Marquez maintained his lead and coasted to victory, moving him to 306 points - seven behind Martin (313), ahead of Sunday's race.
"The target was front row in the qualifying. Starting on first or second was the best place to do a great sprint race," seven-times world champion Marquez said.
"We did a small modification for the sprint race, and I felt much better on the bike."
Aprilia's Martin finished second, but was demoted to third behind LCR Honda's Diogo Moreira.
The Spaniard had found it hard going towards the end of the sprint as he was put under pressure by Tech3's Enea Bastianini, with the thrilling duel leading both riders to stray outside the track.
"I tried in the last lap to do everything I could to keep Enea behind. I achieved that," Martin said.
"I don't know exactly where I touched (the outside), because I was really focused on not doing it. So, big mistake."
Brazilian Moreira earned his first sprint podium. It was also the first sprint podium for satellite team LCR since 2023.
"Today was the day. We saw the crash and I said, 'OK, today I will try to push to see'. At the end, lap by lap, I was feeling more comfortable with the bike," the 22-year-old said.
KTM's Pedro Acosta, fresh off the first MotoGP victory of his career, started in the front row but quickly found himself in the gravel after being involved in a three-rider crash along with Alex Marquez and Fabio Di Giannantonio.
Japan's Ai Ogura (Trackhouse) finished fifth, ahead of Martin's Aprilia teammate Marco Bezzecchi, whose outside bid for the championship was dealt another blow.