The world number one moved ahead of Martina Navratilova for most match wins in a major by a woman, and tied Roger Federer’s mark for men with a 6-2 6-1 victory over Sweden’s Johanna Larsson.
“That’s pretty awesome and what a place to do it, where everything first started,” said the 34-year-old.
Serena won her first Grand Slam title at Flushing Meadows in 1999.
The American is bidding to claim a 23rd Grand Slam singles title, which would see her surpass Steffi Graf as the most successful woman in the Open Era.
The six-time US Open champion, whose number one ranking is under threat, next faces Kazakhstan’s Yaroslava Shvedova, a 6-2 7-5 winner over China’s Zhang Shuai.
Sister Venus Williams, the sixth seed and oldest woman in the tournament at 36, plays Laura Siegemund of Germany later.
Fifth seed Simona Halep of Romania smashed her racquet in frustration before avoiding an upset by defeating Hungary’s Timea Babos 6-1 2-6 6-4.
Halep trailed 3-1 in the deciding set but fought back to reach the last 16.
“I don’t know how I came back. I felt like I didn’t play my best but I was fighting to the end for every ball,” she said.
Halep will play Spain’s 11th seed Carla Suarez Navarro for a place in the quarter-finals.
Suarez celebrated her 28th birthday with a 6-4 6-3 victory over Russian Elena Vesnina.
Fourth seed Agnieszka Radwanska of Poland overcame France’s Caroline Garcia 6-2 6-3 and will face either American Varvara Lepchenko or Ana Konjuh of Croatia next.