Meanwhile, it was business as usual for top seed Daniil Medvedev - who dispatched Arthur Rindeknech in straight sets to reach the Round of 32. Nick Kyrgios, Casper Ruud, Tommy Paul, Karen Khachanov, Matteo Berrettini and 2012 winner Andy Murray were some of the other players who passed the second-round hurdle.
In the women's draw, sentimental favorite Williams was also through to the next round. Other players who did so include Ons Jabeur, Coco Gauff, Madison Keys, Alison Riske and Caroline Garcia.
However, there were upsets galore on the third day of action in New York after a rather serene second day. On that note, here's a look at the top five upsets on Day 3 at the US Open:
#5. Beatriz Haddad Maia (15) lost to Bianca Andreescu (2019 US Open winner) 6-2, 6-4
Beatriz Haddad Maia fell in the second round on her second visit to the US Open. The 15th seed struggled to get going against 2019 winner Bianca Andreescu, winning only six games in the match.
Unseeded at Flushing Meadows this year, the 48th-ranked Andreescu played a solid match, hitting fewer winners (11-20) as well as fewer unforced errors (14-30) to roll into the third round. Haddad Maia was the form player, winning titles in Nottingham and Birmingham and reaching the final in Toronto but came up short against Andreescu.
The Canadian will now take on Frenchwoman Caroline Garcia as she seeks to return to the second week at the US Open.
#4. Leylah Fernandez (14) lost to Ludmilla Samsonova 6-3, 7-6(3)
Another seeded player - another left-hander - fell by the wayside on the third day in New York, as last year's finalist Leylah Fernandez lost in straight sets to Ludmila Samsonova.
After making a surprise run to the title match last year, the 14th seed opened her campaign with a win over Oceane Dodin. However, she came up short against Samsonova, who was impeccable on both serve and return.
The Russian faced some resistance in the second set - seeing five match points come and go - as Fernandez forced a tiebreak. However, Samsonova regained control of proceedings, dropping only three points to move into the third round.
Samsonova will next take on Aleksandra Krunic for a place in the second week, where six-time winner Serena Williams could lie in wait.
#3. Felix Auger-Aliassime (6) lost to Jack Draper 6-4, 6-4, 6-4
It was not all doom and gloom for the left-handers on Wednesday, as Jack Draper, 20, upset last year's semifinalist Felix Auger-Aliassime in straight sets.
The sixth seed - touted as one of the dark horses for the title - never got going against Draper. The left-hander was solid on serve against Auger-Aliassime, winning 36 of his 43 first-serve points.
Draper eventually brought up the second top-ten win of his young career, having beaten World No. 5 Stefanos Tsitsipas in Montreal a few weeks ago.
Making his US Open debut, the 20-year-old has now joined compatriots Andy Murray and Cameron Norrie in the Round of 32. Daniel Evans will make it a quartet of Brits in the third round if he beats James Duckworth later tonight (Thursday).
Meanwhile, Draper will look to continue his giant-killing ways against 27th seed Karen Khachanov on Friday as he seeks a place in the second week.
#2. Maria Sakkari (3) lost to Xiyu Wang 3-6, 7-5, 7-5
Maria Sakkari's wait for a maiden Major title continues, as she came up short in a three-set thriller against Xiyu Wang on Wednesday.
The third seed started strong - taking the opener for the loss of just three games. In a tight second set, Wang twice squandered a break of serve before a Sakkari double fault leveled the proceedings.
It was the left-hander's turn to flip the script in the decider - recovering from a 3-1 deficit to reach the third round at a Major for the first time - as Sakkari's 12 double faults proved costly on the night.
Wang will next take on Alison Riske-Amritraj on Friday for a place in the second week.
#1. Anett Kontaveit (2) lost to Serena Williams (six-time US Open winner) 7-6, 2-6, 6-2
Anett Kontaveit was the highest seed to fall on the third day of action at the US Open.
Facing the retiring Serena Williams, Kontaveit dropped a tight opening set in a tiebreak. However, she silenced the partisan crowd by conceding only two games to win the second set and force a decider.
Williams - a six-time winner in New York - regained control of the proceedings. After saving a break point at 4-2, she breezed past the finish line as a record crowd of 29,959 on Arthur Ashe erupted in jubilation.
"I don't have anything to prove. I don't have anything to win. I have absolutely nothing to lose," said Williams, trying to temper expectations of an unlikely title run.
Nevertheless, Williams knows she will be expected to do an encore against Ajla Tomljanovic - another player she has never faced before - as she sets sights on a record seventh US Open title.
Also Checkout:- US Open 2022 Schedule