The world number one has never lost before round three at the US Open and, with Beyonce and Jay-Z watching on in Arthur Ashe Stadium, she was delighted to reach Navratilova's mark.

"Sometimes I don't even know that I'm hitting these milestones," Williams said.

"But some of them I'm really proud of. Like this one's kind of cool, to win 306. That's really a cool milestone.

"Martina was just an incredible legend. For me, one of the best players to ever play tennis.

"Someone that I never even thought I could be as good as numbers-wise. So, yeah, that's what I think of her."

Williams is bidding to achieve another milestone in New York, where success would see her overtake Steffi Graf's Open-era record 22 grand slam singles titles.

The top seed was not at her blistering best against her King, making 28 unforced errors, but this was her second straight-sets victory and she was in control throughout.

"I just think it should have been a different scoreline for me. I feel like I made a lot of errors," Williams said.

"I just didn't have a great day today. But it's always good to get a win when you're not playing well. I definitely don't think I played the way I did in my first round."

Williams will now face Sweden's Johanna Larsson for a place in the last 16 and the 34-year-old insists her troublesome right shoulder is still holding up.

"It's stable. I just got to keep it like that," Williams said.

"It's two matches in, and usually you want to be able to play seven matches. It's not even close to the halfway point.

"I definitely want to keep it as good as it can be."

Elsewhere, Serena's sister Venus also progressed, along with fourth seed Agnieszka Radwanska and fifth seed Simona Halep.