The world No1 overpowered her American opponent, who was just two years old when Williams won her first Miami title.
“It was tough. She’s young, and her being an American and her just doing so well, you want to see people like her do well,” said Williams, who will next face Svetlana Kuznetsova.
“So when you’re up against them you have to kind of put that aside, even though I’m always cheering for her. But I have to put it aside and just play the match.
“If you break down her age and ability and how well she handled the moment, it was good.”
Meanwhile, Venus Williams is preparing for a fourth-round clash with Caroline Wozniacki after beating Sam Stosur.
Venus and sister Serena have 10 Miami titles between them, and are age 33 and 34. Serena is on a 14-0 run in 2015, while Venus is 17-3.
MORE: The latest football news
MORE: The latest tennis news