Williams, the tournament defending champion, ran her personal winning streak to 33 matches with a 6-3, 6-2 decision over Caroline Garcia after Radwanska posted an early 6-1, 6-3 romp past Mathilde Johansson.
Williams dropped only eight points in eight games serving. She had nine aces and no double faults in a match in which she committed just nine unforced errors. She broke Garcia's serve in four of the nine receiving games.
Radwanska finished off five of her nine break opportunities in advancing to the third round. Johansson did manage a break in the second set but Radwanska won half the points off Johansson's serve in the set.
Williams next faces Kimiko Date-Krumm, 42, who is the oldest woman to reach Wimbledon's third round in the Open Era. Date-Krumm stopped Alexandra Cadantu 6-4, 7-5 on Thursday.
Radwanska's third-round foe is Madison Keys, who used a 6-4, 6-2 win over 30th-seeded Mona Barthel to reach a Grand Slam third round for the third time this year. She's never made it to the fourth round, however.
No. 6-seeded Li Na took a seesaw 6-2, 1-6, 6-0 decision over Simona Halep, while 11th-seeded Roberta Vinci beat Jana Cepelova 6-1, 4-6, 9-7 and 14th-seeded Samantha Stosur defeated Olga Puchkova 6-2, 6-2.
Marina Erakovic knocked off 24th-seeded Peng Shuai 7-6 (8-6), 6-2.
Seeded players winning second-rounders Thursday included No. 18 Dominika Cibulkova, No. 23 Sabine Lisicki and 32nd-seeded Klara Zakopalova. Unseeded Tsvetana Pironkova and Petra Martic also won matches Thursday.