"I didn't really play worse these sets but he showed what he's capable of and that's why it was really tough ... in these matches you need a little bit of luck, from time to time it's really close", the 27-year-old added.
Stephens, the 2017 US Open champion who once reached the dizzy heights of world no.3, came out confidently firing on all cyclinders with thunderous groundstrokes and exceptional pace to send the 38-year-old racing around the court like a headless chicken. In the final set, the six-time champion dropped six points on serve, mounting the pressure on the other side of the net with two comfortable holds in the early stages. "That's most like the tactic with most of the players that I play".
Williams double-faulted at deuce but, staring at a potential exit, shifted through the gears to deliver a pair of unstoppable serves to regain the lead.
Brady, who is one of four American women still alive in singles, will face either Petra Martic or Yulia Putintseva in her first Grand Slam quarterfinal match. The game completely changed in the second set when Serena played well and earned a break for 4-2.
Williams is seeking a record-equalling 24th singles Grand Slam title at a subdued, spectator-free Billie Jean King US National Tennis Center in NY. We always play some incredible matches and it brings outthe best of my fitness when I play Sloane.
Last week, Williams shared a sweet Instagram snap of her mini-me watching courtside.
She will take on 15th-seeded Maria Sakkari of Greece in the last 16, who stunned Williams at last month's Western & Southern Open.
Greek Sakkari accounted for 22nd seed Amanda Anisimova 6-3 6-1.
Mladenovic was one of seven players placed under extra restrictions during the tournament after contact tracing determined she potentially could have been exposed to COVID-19 by Benoit Paire, the only entrant to test positive.
Unranked Bulgarian Tsvetana Pironkova extended her US Open giant-killing run on Saturday, scoring a second consecutive upset with a straight-sets defeat of 18th seed Donna Vekic. "Otherwise there is no chance against her", Sakkari said of playing Serena.
Karolina Muchova is next after the 20th seed prevailed 6-3 2-6 7-6 (9-7) against Sorana Cirstea.
"So I just try to think about how fortunate I am to have been in this position, and honestly, to be Serena".
But six-time victor Williams overcame early nerves to fight to win 2-6 6-2 6-2 in one hour and 43 minutes to reach the fourth round.