On Sunday, Williams entered the US Open quarters for the 16th time in her career with a straight-sets win over Petra Martic of Croatia at an electric Arthur Ashe Stadium.
The 23-time Grand Slam women's singles champion defeated Martic 6-4, 6-3 to set up a last-eight date with China's Wang Qiang, who stunned No.2 seed Ashleigh Barty 6-2, 6-4 in one hour and 22 minutes, to move into her maiden Grand Slam quarter-final.
Martic had never been past the second round of the US Open in seven trips to Flushing Meadows, and her lack of big-match experience proved costly, as Williams gained momentum and never took her foot off the pedal.
"I feel fine right now physically and obviously my state is super intense," Williams said in the on-court interview after the match. "I'm always incredibly intense. I am just trying to keep moving forward."
No. 5 seed Svitolina stunned No. 10 Madison Keys 7-5, 6-4 to move into last eight of the competition.
Svitolina will now face another first-timer in the last eight, No. 16 seed Johanna Konta of England, who rallied past No. 3 Karolina Pliskova of the Czech Republic, 6-7, 6-3, 7-5.
Both the players have faced each other four times over the years, and the Ukrainian holds a 4-0 record against the Brit.
( With inputs from IANS )