The Puerto Rican made short work of Rodriguez for his 31st knockout victory, and then turned the spotlight onto trainer Roach for his efforts in the build-up to the fight.
"I'm very happy to have Freddie in my corner, we were able to get back to basics," Cotto told reporters.
"It feels good to win and be able to do it in front of a wonderful crowd. All of the work that we put in over the last month really showed tonight.
"I thought I hit him with some good shots early and I was able to get the stop."
The win was Cotto's first fight since a points loss to Austin Trout last December.