Cotto, with a ferocious left hook and punishing combinations, knocked Martinez down three times in the first round, and continued to dominate the scheduled 12-round bout at Madison Square Garden.
Martinez’s corner waved an end to the fight as the bell rang for round 10.
The Argentine, who wore supportive sleeves on both his knees, was cut near his right eye and over his left eye and his knees buckled several times during the one-sided contest.
Cotto, 33, became the first Puerto Rican ever to win titles in four different weight divisions after previously holding the junior welterweight, welterweight and super welterweight crowns.
“This is the biggest achievement I ever had in my career,” said Cotto, who improved to 39-4 while the 39-year-old Martinez fell to 51-3-2.
Martinez said he never recovered from Cotto’s stunning start.
“I got hit and I never recovered after that. I tried my best,” said Martinez, speaking through a translator. “He caught me cold, he caught me hard at the beginning and I didn’t recover from it.”
Martinez looked set to continue, despite buckling after another powerful left in the ninth round that the referee ruled a knockdown even though the Argentine did not touch the canvas. But his corner surrendered.
“More than a boxer, he’s my brother and he’s my friend,” said trainer Pablo Sarmiento.
Freddie Roach, Cotto’s trainer, said the winner executed the game plan to perfection.
“I’m really proud of him,” Roach said. “We had a great game plan and he followed it to a tee.”
Roach said Cotto manoeuvred Martinez masterfully.
“He had him moving into the hook all night long,” Roach said. “Miguel is a better boxer than Martinez.”
Cotto landed twice as many punches in the bout and also proved to be the bigger puncher even though he was fighting at the 160-pound limit for the first time in his career.
Martinez, 39, has had physical ills to contend with, showing the effects of shoulder and knee operations in holding off Briton Martin Murray in a battle last April in Buenos Aires despite being knocked down in the eighth.
The loser did not attend the post-fight news conference.
“Sergio said he had no excuses,” Lou DiBella, the fighter’s promoter, told reporters. “After that first round, he felt dizzy throughout the fight but he wanted to continue.
“But obviously he was taking a terrible beating.”
(Reporting by Larry Fine; Editing by Julian Linden/Sudipto Ganguly)