The 41-year-old Williams has won seven major titles, including victories at Flushing Meadows in 2000 and 2001
It was a day of mixed fortunes for the Williams family at the Emilia-Romagna Open, while Lisa Pigato had a debut to remember despite suffering defeat.
Angelique Kerber was among the seeds to tumble out of the Australian Open, but there was no such trouble for her fellow major winners
A five-time singles champion at the All England Club Williams beat Mihaela Buzarnescu of Romania 7-5, 4-6, 6-3.
Zarina Diyas got the better of "legend" Venus Williams at the Miami Open, while there were wins for Shelby Rogers and Ajla Tomljanovic
Serena Williams and second seed Sofia Kenin flew the American flag on day two of the US Open, while Garbine Muguruza also made a winning start in New York
The Gentlemen's and Ladies' singles winners at Wimbledon will each get USD 2.4 million, a nearly 28 percent decrease from the 2019 edition
Serena Williams will face sister Venus in the Top Seed Open second round after contrasting wins on Tuesday
The tournament, featuring a strong field including world number one Ashleigh Barty and Australian Open champion Naomi Osaka, gets underway on January 6
Cori Gauff showed astonishing maturity to secure a sensational victory over her idol and five-time champion Venus Williams on day one at Wimbledon.
Ahead of a Wimbledon first-round clash with one of her idols, Venus Williams, here is a close look at American teenager Cori 'Coco' Gauff
Big stars in tennis are having very bad games. Novak Djokovic was out on the first day, now Serena and Venus.