Chavez, who blamed his early struggles on leg cramps, landed a right uppercut before unleashing a flurry of shots to end the bout two minutes and 21 seconds into the seventh.
“I began by studying him,” Chavez said. “I saw he had nothing and I dove in.
“He’s strong, he’s young, he’s big. He gave me everything he had but he couldn’t do anything to me.”
After failing to throw a punch for the first 75 seconds of the fight and absorbing some early pressure from Lee, Chavez became increasingly emboldened as the bout developed.
In the fifth round the Mexican even taunted Lee, dropping his gloves, grinning and pretending to have wobbly knees.
The victory puts Chavez in line for a title-unification fight with recognised world middleweight champion Sergio Martinez.
“Martinez moves a lot,” the Mexican said. “That’s a fight I have to make.”