World number one Williams dominated Sweden's Johanna Larsson 6-2, 6-1 to surpass Martina Navratilova for most Grand Slam wins by a woman with 307.
Not only has she surpassed Navratilova, she matched Roger Federer's mark for men.
"To be up there with both men and women is something that's super-rare, and it actually feels good," said Williams, who said she was "really excited" to reach 307.
"Obviously I want to keep that number going higher," added Williams, who will get her chance when she takes on Kazakhstan's Yaroslava Shvedova for a quarter-final berth.
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"It definitely feels solid," she said. "I'm doing a lot of work on it so I can keep it in this position."
While Williams encountered little resistance, it was another story for the top men's seeds in action.
Wawrinka, a two-time Grand Slam winner and twice a semi-finalist in New York, had the closest call, saving a match point in a 4-6, 6-3, 6-7 (6/8), 7-6 (10/8), 6-2 victory over Britain's Dan Evans.
The 31-year-old third seed saved the match point at 5/6 in the fourth set tiebreaker, breaking the will of his 64th-ranked opponent.
Many of Murray's troubles against Paolo Lorenzi were of his own making as he allowed the energetic Italian journeyman to make him look ordinary through two sets before pulling himself together to win 7-6 (7/4), 5-7, 6-2, 6-3.
"I had to stop rushing," said Murray, who arrived at the year's final Grand Slam off victories at Wimbledon and the Rio Olympics and may have expected less from Lorenzi, the 34-year-old who only won a first ATP title in July.
Murray takes on Bulgarian Grigor Dimitrov, a 6-4, 6-1, 3-6, 6-2 winner over Portugal's Joao Sousa, for a quarter-final berth.
Wawrinka next faces 63rd-ranked Ukrainian Illya Marchenko, who advanced when a hurting Nick Kyrgios, hobbled by a painful right hip, retired while trailing 4-6, 6-4, 6-1.
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The tall Croat started to serve better, losing only five points in his next five service games. He also attempted to keep the points short but Kovalik continued to present a dogged fight and it boiled down to tie-breaker with the two players holding their serves.
Stunned by the reversal, the Croat put his foot on the gas and raced to a 3-0 lead with a break in the second game.
After a foot fault call at 15-15, which perhaps disturbed his rhythm, Kovalik hit a forehand long at 30-40 to face a break point. Cilic played smart and pinned the Slovakian on the far left side of the baseline in a long rally and sent down a volley winner from a weak backhand return to seal the break.
The Slovakian though choked when he was serving to stay in the match at 5-6. He sent a backhand to net to hand Cilic his first set point and followed that with a long forehand to allow the Croat make a comeback in the match.
The third set was again neck and neck before Kovalik cashed in on unforced errors from Cilic to get a break in the 11th game, setting himself up to close the match in his favour.
In another second match of the day, Spaniard Albert Ramos-Vinolas outplayed Steve Darcis 6-2 6-0.