The victory means that Serena has now won 308 Grand Slam matches, a record.
The 22-time Grand Slam winner meets the Romanian fifth seed Simona Halep next up.
Her sister Venus, the oldest player left in the tournament, came unstuck against the Czech Karolina Pliskova.
Venus won the first set then the Czech claimed the second set before the decider went to a tie-break.
Pliskova wins 4-6 6-4 7-6.
Andy Murray in the form of his life made light work of a potentially tricky match against Bulgarian Grigor Dimitrov.
Murray won 6-1 6-2 6-2 and delivered the fastest serve of his career at 226 km/h.
Murray meets Kei Nishikori next.
Another form player, Argentina’s Juan Martin Del Potro, is through to the quarters.
He was 6-3 3-2 up when his Australian opponent Dominic Thiem retired with an injury.
Del Potro plays Stan Wawrinka next. (Euronews)