Angelique Kerber, Simona Halep and Venus Williams avoided upset losses to reach the Miami Open third round on Saturday (AEDT).

Kerber, back as world No.1, was pushed before beating Duan Ying-ying at the WTA Premier event.

Like the German, Williams had a straight-sets win, while Halep went the distance to get past Naomi Osaka.

Numerous seeds did make early exits, with Indian Wells champion Elena Vesnina and semi-finalist Kristina Mladenovic among them.

Kerber has made a slow start to the year, but battled to a 7-6 (7-3) 6-2 win over Duan.

The two-time grand-slam champion was almost punished for missed chances in the first set before a more convincing second.

Kerber ended up converting just four of 15 break points for the match, a rate she will need to improve in a third-round meeting with Shelby Rogers.

Williams is a three-time winner in Miami, but the last of those titles came in 2001.

However, the veteran American booked her spot in the third round with a 6-4 6-3 victory over Brazil's Beatriz Haddad Maia.

Williams served nine double faults but was fortunate, saving five of six break points.

Halep, the No.3 seed, battled past the talented Osaka 6-4 2-6 6-3 in just under two hours.

The Romanian dominated the third set, losing just nine points on serve to see out her win.

Garbine Muguruza, Svetlana Kuznetsova, Madison Keys, Johanna Konta and Sam Stosur were also among the winners.

Numerous seeds departed, however. Vesnina, who won Indian Wells, made an early exit with a surprise 3-6 6-4 7-5 loss to wildcard Ajla Tomljanovic.

Mladenovic went down to qualifier Patricia Maria Tig, while Daria Kasatkina, Carla Suarez Navarro, Roberta Vinci, Ekaterina Makarova, Caroline Garcia, Timea Babos, Irina-Camelia Begu and Anastasija Sevastova all fell.