The 38-year-old American dropped the opening set before staging a comeback to seal a 2-6 6-2 6-2 victory and set up a fourth-round meeting with Greek Maria Sakkari, who beat Williams at the Western & Southern Open last month
Serena Williams survived a third-round scare to defeat 2017 champion Sloane Stephens and stay on course for a record-equalling 24th Grand Slam title.
The 38-year-old American dropped the opening set before staging a comeback to seal a 2-6 6-2 6-2 victory and set up a fourth-round meeting with Greek Maria Sakkari, who beat Williams at the Western & Southern Open last month.
Also advancing in the women's draw was second seed Sofia Kenin, who overcame a sluggish start to beat Tunisian Ons Jabeur 7-6(4) 6-3 and move into the fourth round for the first time.
Former world number one Victoria Azarenka breezed past Iga Swiatek 6-4 6-2 while Belgian Elise Mertens defeated Caty McNally 7-5 6-1.
Seventh seed Madison Keys dropped the opening set to France's Alize Cornet before retiring early in the second set with a neck injury.
In the men's draw, Austrian second seed Dominic Thiem staved off a spirited fightback from Marin Cilic to beat the former champion 6-2 6-2 3-6 6-3.
Thiem will next face Canadian Felix Auger-Aliassime, who made it to the last-16 of a Grand Slam for the first time with a 6-1 6-0 6-4 win over France's Corentin Moutet.
Daniil Medvedev, last year's runner-up, crushed American J.J. Wolf 6-3 6-3 6-2 while Australia's Alex de Minaur recovered from a second-set 'bagel' to beat 11th seed Karen Khachanov 6-4 0-6 4-6 6-3 6-1.
KENIN SAILS INTO LAST-16
Second seed Sofia Kenin secured a spot in the fourth round of the U.S. Open for the first time in her career with a 7-6(4) 6-3 victory over Turkey's Ons Jabeur. Kenin will next face 16th seed Elise Mertens.
KEYS RETIRES WITH NECK ISSUE
American Madison Keys, the 2017 runner-up, dropped the opening set of her third-round encounter against Frenchwoman Alize Cornet before retiring with a neck injury. Cornet was leading 7-6(4) 3-2 when Keys decided she was unable to continue.
AUGER-ALIASSIME INTO LAST-16
Felix Auger-Aliassime eased into the last-16 of a Grand Slam for the first time in his career with a convincing 6-1 6-0 6-4 win over France's Corentin Moutet.
The Canadian youngster will play the winner of the match between second seed Dominic Thiem and 2014 champion Marin Cilic.
THIEM PASSES CILIC TEST
Second seed Dominic Thiem overcame a mid-match wobble to defeat Croatian Marin Cilic 6-2 6-2 3-6 6-3 and set up a fourth-round clash with Felix Auger-Aliassime.
"Today was a good win against a great champion and a good player and that should give me a boost."— Sky Sports (@SkySports) September 6, 2020
Is Dominic Thiem the main challenger to Novak Djokovic?
BERRETTINI AND PIRONKOVA THROUGH IN STRAIGHT SETS
Sixth seed Matteo Berrettini beat Casper Ruud 6-4 6-4 6-2, firing 40 winners and 13 aces past the Norwegian to set up a last-16 encounter with Russian 10th seed Andrey Rublev.
Bulgaria's Tsvetana Pironkova, playing her first tournament in three years, continued her dream run by beating Croatian Donna Vekic 6-4 6-1 in 64 minutes to move into the last-16.
MLADENOVIC-BABOS WITHDRAWN FROM DOUBLES DRAW
Top seeds Kristina Mladenovic and Timea Babos were withdrawn from the U.S. Open women's doubles competition after Mladenovic received a COVID-19 quarantine notice from public health officials, the tournament organisers said.
Mladenovic is one of 10 players who came in contact with France's Benoit Paire, who pulled out of the tournament after testing positive for the novel coronavirus.
SERENA SEALS COMEBACK WIN
Third seeded Serena Williams rallied from a set down to beat fellow American Sloane Stephens 2-6 6-2 6-2 in a clash of former champions.
POSPISIL, DE MINAUR THROUGH TO LAST-16
Canada's unseeded Vasek Pospisil overcame a mid-match blip to score an upset 7-5 2-6 4-6 6-3 6-2 win over Spain's eighth seed Roberto Bautista Agut.
Pospisil will next face Australian Alex de Minaur, who also needed five sets to put away 11th seed Karen Khachanov of Russia.
MEDVEDEV CRUISES INTO FOURTH ROUND
Russian Daniil Medvedev, the 2019 runner-up, eased into the last 16 with a 6-3 6-3 6-2 win over American wildcard J.J. Wolf.
Third seed Medvedev, chasing a maiden Grand Slam title, is yet to drop a set at this year's tournament at Flushing Meadows.
Sakkari makes quick work of Anisimova at US Open https://t.co/FedfO6gWEs— TOI Sports News (@TOISportsNews) September 5, 2020
SAKKARI ELIMINATES ANISIMOVA IN 55 MINUTES
Greek 15th seed Maria Sakkari was at her phenomenal best when she beat American Amanda Anisimova 6-3 6-1 in a match that lasted less than an hour at Louis Armstrong Stadium.
Sakkari fired four aces and 11 winners past the 22nd seed, breaking her five times while Anisimova also made 28 unforced errors.