World number four Williams ran out a 6-4 winner in the opening set, before easing into round four thanks to a 6-0 bagel in the second set.
Reflecting on her display, Williams confessed that it was nice to have beaten a player that had knocked her out of the Australian Open earlier this year.
"It was better today," Williams said. "I played such a good opponent, she beat me in Australia, so I knew I needed to play better going into today and I definitely felt I played better.
"Mentally I am just going with the flow, this is my home crowd and it's hard not to be excited to play here, being an American and playing in New York."
The 30-year-old won 32 of the 40 points she served during today's match.