Williams defeated Danka Kovinic of Montenegro, winning 6-3 6-3. Williams will retire after the competition.
A nearly complete 25,000-person Arthur Ashe Stadium audience yelled at their hero, who reacted with trademark tenacity.
On Wednesday, Williams, 40, will face Anett Kontaveit, the second-seeded Estonian.
In addition to participating in the doubles with her elder sister Venus, the 23-time Grand Slam singles winner, one short of Australian Margaret Court’s record, is extending what she hopes would be a protracted farewell this weekend.
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She had to defeat Kovinic, who was ranked 80th in the world. There was a loud cheer when she converted the first of her three match points to guarantee that her singles career would continue.
Williams sprang to her feet when Kovinic’s backhand return struck the net. She spun ecstatically in the middle of the court before returning to her seat to take it all in and blew kisses to her adoring supporters.
She said that events like these impacted her intentions “I still find it very challenging since I like being outside.
“I feel more like I can fit in with the world the more competitions I participate in. The knowledge that you can shine more if you keep doing it is a complex sensation.
“But I need to advance to the next thing; you know. There are a lot of other things I want to accomplish, so I believe it’s crucial.”
