Serena Williams, who recently won singles and doubles titles at both Wimbledon and the Olympics, rolled to a 6-2, 6-4 victory over Maria Jose Martinez Sanchez. That will send her into the third round for a meeting with Ekaterina Makarova, who disposed of Elena Vesnina 6-3, 6-4.
Venus Williams, however, fell to Kerber 6-2, 5-7, 7-5 in a match that did not end until after midnight. Kerber is seeded sixth in this tournament.
Radwanska survived her second-round match against Suarez Navarro 4-6, 6-3, 6-0 and will now meet Jelena Jankovic, a former world No. 1 who downed Lara Arruabarrena Vecino 6-4, 6-2. Radwanska reached the finals at Wimbledon this year before losing to Serena Williams.