Marquez pushed pole-sitter Martin into second place in Motegi after overtaking his fellow Spaniard midway through the race.
It put seven-time world champion Marquez back within touching distance of the championship lead after losing ground in the previous race in Austria.
Marquez completed the double after also winning Saturday's sprint race in Japan.
He said it was "very important" to claim maximum points from the weekend.
"The race was tough, especially when I was behind Jorge, but I knew that if I was able to lead the race the pace was good," he said.
"Jorge tried to attack but then I just increased the pace and it was enough to do the last two laps more relaxed."
Italian Marco Bezzecchi finished third and slipped further behind in the title race.
Marquez dropped to the tarmac to fire off a round of press-ups before the race in a new warm-up routine.
The Ducati rider then flexed his muscles on his bike, biding his time behind Martin before making his move in lap 11.
Martin said he had "a good package to fight for the rest of the season" but admitted that Marquez was the better rider on the day.
"I think today to win was really difficult," said Martin.
"It was one of the days when I rode almost perfectly, I was really smooth, really confident, and even then I couldn't win."
It was Marquez's sixth grand prix win of the season, despite missing the races in Le Mans and Catalonia to undergo surgery on his foot and shoulder.
A sunny day in Japan clouded over and cooled considerably shortly before the race but the rain held off.
Marquez never looked in any trouble once he had gone past Martin, who in turn looked comfortable in second place.
Bezzecchi had to fight a furious rearguard action to hold off fellow Italia Enea Bastianini, who finished fourth.
Spain's Pedro Acosta, who chalked up his first ever victory in MotoGP in Austria, finished seventh.
Ai Ogura, who was bidding to become the first Japanese race winner in Motegi since 2004, was sixth.
Brazil's Diogo Moreira, who finished second in the sprint when Martin was demoted to third due to a penalty, crashed out of the grand prix.