Second-seeded Roger Federer had a blip of his own, losing his first set of the tournament, but he recovered to beat Lloyd Harris of South Africa, 3-6, 6-1, 6-2, 6-2.
Third-seeded Rafael Nadal advanced to a second-round meeting with Nick Kyrgios with a 6-3, 6-1, 6-3 victory over Yuichi Sugita of Japan. Fifth-seeded Dominic Thiem, a finalist at the French Open last month, lost to the American Sam Querrey, 6-7(4) 7-6(1) 6-3 6-0. The No. 6 and No. 7 seeds in the men’s draw, Alexander Zverev and Stefanos Tsitsipas, were eliminated in the first round Monday.
Williams and several other women playing Tuesday are in a quarter that has been called the Group of Death. Among them is the top seed and a recent French Open champion, Ashleigh Barty, who won her first match as the top-ranked woman, 6-4, 6-2, against Zheng Saisai, 6-4, 6-2. The defending women’s champion, Angelique Kerber, also advanced, defeating Tatjana Maria, 6-4, 6-3.
That quarter started with seven Grand Slam champions in it, but it lost two on Tuesday. Garbiñe Muguruza, the 2017 Wimbledon champion, fell to the Brazilian qualifier Beatriz Haddad Maia, 6-4, 6-4. Maria Sharapova, who served for the match while leading by 5-3 in the second, retired from her match with a left wrist injury while trailing Pauline Parmentier of France, 4-6, 7-6 (4), 5-0.
There had been plenty of speculation about Williams’s readiness going into this match. She was a finalist at last year’s Wimbledon and United States Open after returning in March from the birth of her daughter, but she has not been in peak form this season. At 37, she has battled ankle and knee injuries and played a truncated schedule.