American wild card Catherine Bellis, the youngest player in the draw, took her place alongside the five-times US champion by stunning 12th seeded Australian Open finalist Dominica Cibulkova of Slovakia 6-1 4-6 6-4.
Williams advanced 6-3 6-1 over unseeded fellow American Taylor Townsend as she followed Federer onto the Arthur Ashe Stadium court to cap the second day of the championships.
Should she go on to win the tournament, the two-times defending champion would join Chris Evert and Martina Navratilova in fourth place on the all-time list of women's Grand Slam singles champions with 18 titles apiece.
"Hopefully, I can just build on this," said Williams, who has had a disappointing Slam season with her best result a fourth-round exit at the Australian Open back in January.
Margaret Court (24), Steffi Graf (22) and Helen Wills Moody (19) are the only three women to have won more Grand Slam titles.
Other leading contenders were keen to display their skills on a sunny day in Flushing Meadows.
Wimbledon champion Petra Kvitova and runner-up Eugenie Bouchard launched their Open campaigns with a bang, blasting by their respective first-round opponents with a minimum of fuss.
They were joined in the second round by eighth-seeded former world number one Ana Ivanovic, 11th-seeded Italian Flavia Pennetta, 16th seed Victoria Azarenka and 2011 champion Sam Stosur, but the biggest jolt of energy was supplied by Bellis.
Playing on the secondary Court Six, the teenager added her name to the record books by becoming the youngest female to win a match at the US Open since Anna Kournikova in 1996.
"I went into the match thinking it was going to be such a great experience," said the pony-tailed Bellis, who received her wild card when she became the youngest player to win the girls' 18s national championships since Lindsay Davenport in 1991.
"But I never thought I would come out on top winning. I'm still in shock about that match."
Third-seeded Kvitova of the Czech Republic crushed Kristina Mladenovic of France 6-1 6-0, while Bouchard was nearly as efficient in dismissing Olga Govortsova of Belarus 6-2 6-1 in the afternoon sunshine.
"I'm very happy. First round is always nerves," said the hard-hitting Kvitova, who won the lead-in tournament in New Haven last weekend. "It was the same today. When I wake up, I start to feel nervous. I was just glad how I played today."
Kvitova fell at the first hurdle here after winning her first Wimbledon crown in 2011.
"The other Grand Slams are a big challenge for me right now. I remember 2011 when I lost my first round after winning Wimbledon, so I'm just glad that I'm better already," she said with a smile.
The 20-year-old Bouchard, the only woman to reach the semi-finals of the year's first three Majors, answered questions over her hardcourt form with an overwhelming win.
Seventh-seeded Bouchard, who won one match in three events since losing to Kvitova at the All England Club last month as she was bothered by knee and hamstring injuries, ripped 19 winners and forced 24 errors from an outclassed Govortsova.
"Obviously I would have liked more matches, but that's the way it is sometimes," said the aggressive baseliner.
"I still feel very confident with myself."
Canada's Eugenie Bouchard hits a return to Olga Govortsova of Belarus (Reuters)
They were joined in the second round by eighth-seeded former world number one Ana Ivanovic, 11th-seeded Italian Flavia Pennetta, 16th seed Victoria Azarenka and 2011 champion Sam Stosur.
Failing to follow a procession of seeds into the second round was former French Open champion Svetlana Kuznetsova of Russia. The 20th seed was upset by 82nd-ranked Marina Erakovic of New Zealand 3-6 6-2 7-6 (3).
Former champion Stosur carried her recent momentum into New York with a first-round win that extended a perfect record for Australians to five-for-five before a loss by Ashleigh Barty to Barbora Zahlavova Strycova of Czech Republic ended the streak.
Stosur pushed past 49th-ranked American Lauren Davis 6-1 6-4 to put behind her a shock, first-round ouster at Flushing Meadows last year to American qualifier Victoria Duval.
The win by 21st-ranked Stosur, only the third player to beat Serena Williams in a Grand Slam final, continued a turnaround after six losses to opponents ranked outside the top 60 had dropped her out of the top 20 for the first time in five years.
Last week, the hard-hitting Australian showed signs of a revival. The 30-year-old Stosur beat Bouchard in New Haven before eventually falling to Kvitova in the semi-finals.
"I am feeling good," she said. "Going to Connecticut last week and playing well there and making semis, I think it's a huge boost. I couldn't really be pleased more with the way that I have had this lead-up."
Ivanovic showed off her self-assured hard court form with a 6-3 6-0 rout of American Alison Riske, who had lost to the Serb 7-5 7-6 this year in New Zealand.
"It was very tough first-round match. We had a tough one in Auckland," said Ivanovic, who has wins over Serena Williams and Maria Sharapova in battling back into the world top 10.
"The confidence is on a high level," said Ivanovic. "I had a great season behind me."
US Open results
3-Petra Kvitova (Czech Republic) beat Kristina Mladenovic (France) 6-1 6-0
Vania King (U.S.) beat Francesca Schiavone (Italy) 6-3 3-6 6-3
Varvara Lepchenko (U.S.) beat Alison Van Uytvanck (Belgium) 7-5 6-2
Mona Barthel (Germany) beat 32-Zhang Shuai (China) 6-1 6-2
24-Samantha Stosur (Australia) beat Lauren Davis (U.S.) 6-1 6-4
Kaia Kanepi (Estonia) beat Pauline Parmentier (France) 7-6(3) 3-6 6-1
Coco Vandeweghe (U.S.) beat Donna Vekic (Croatia) 2-6 6-3 6-1
15-Carla Suarez Navarro (Spain) beat Ajla Tomljanovic (Australia) 3-6 6-2 6-1
11-Flavia Pennetta (Italy) beat Julia Goerges (Germany) 6-3 4-6 6-1
Shelby Rogers (U.S.) beat Maryna Zanevska (Ukraine) 6-4 6-3
Nicole Gibbs (U.S.) beat Caroline Garcia (France) 6-2 2-6 6-3
23-Anastasia Pavlyuchenkova (Russia) beat Teliana Pereira (Brazil) 6-2 6-0
29-Casey Dellacqua (Australia) beat Patricia Mayr-Achleitner (Austria) 7-5 6-3
Wang Qiang (China) beat Paula Kania (Poland) 6-2 6-0
Karolina Pliskova (Czech Republic) beat Yvonne Meusburger (Austria) 6-2 6-2
8-Ana Ivanovic (Serbia) beat Alison Riske (U.S.) 6-3 6-0
Petra Cetkovska (Czech Republic) beat Klara Koukalova (Czech Republic) 6-1 2-6 6-3
Aleksandra Krunic (Serbia) beat Katarzyna Piter (Poland) 6-4 6-1
27-Madison Keys (U.S.) beat Jarmila Gajdosova (Australia) 6-0 6-3
Marina Erakovic (New Zealand) beat 20-Svetlana Kuznetsova (Russia) 3-6 6-2 7-6(3)
Elena Vesnina (Russia) beat Chan Yung-Jan (Taiwan) 6-0 7-5
Christina Mchale (U.S.) beat Chanelle Scheepers (South Africa) 6-2 1-6 7-6(5)
16-Victoria Azarenka (Belarus) beat Misaki Doi (Japan) 6-7(3) 6-4 6-1
Catherine Bellis (U.S.) beat 12-Dominika Cibulkova (Slovakia) 6-1 4-6 6-4
Zarina Diyas (Kazakhstan) beat Lesia Tsurenko (Ukraine) 6-1 6-2
Polona Hercog (Slovenia) beat Elina Svitolina (Ukraine) 6-2 7-6(4)
17-Ekaterina Makarova (Russia) beat Grace Min (U.S.) 6-4 6-2
30-Barbora Zahlavova Strycova (Czech Republic) beat Ashleigh Barty (Australia) 6-1 6-3
Monica Niculescu (Romania) beat Yaroslava Shvedova (Kazakhstan) 6-7(5) 6-1 7-5
Sorana Cirstea (Romania) beat Heather Watson (Britain) 6-1 6-1
7-Eugenie Bouchard (Canada) beat Olga Govortsova (Belarus) 6-2 6-1
- Sports & Recreation
- Czech Republic
- Petra Kvitova
- Ana Ivanovic
- Sam Stosur
- Eugenie Bouchard
- Australian Open
- Flavia Pennetta