Serena and Venus also won their opening doubles match, beating Romania's Sorana Cirstea and SimonaHalep 6-3 6-2 to set up a clash with Kerber and Sabine Lisicki.
The Pole's reward for a 6-7 (10-12) 6-4 6-2 success is a match with Argentine qualifier Paula Ormaechea, who claimed the first WTA Tour level match win of her career by beating 50th-ranked Romanian SimonaHalep 6-1 3-6 7-5.
Poland's fourth seed Agnieszka Radwanska was the highest to fall, losing 6-7 6-1 6-2 to SimonaHalep of Romania in the second round, but she may have gained some consolation by seeing sister Urszula inflict defeat on 15th seed Ana Ivanovic.
Twelfth seed Agnieszka Radwanska enjoyed a relatively comfortable passage into the third round with a 6-3 6-4 win over Croatia's Petra Martic, and the Pole will play SimonaHalep after the Romanian beat Russia's 24th seed Alisa Kleybanova 6-4 7-6 (7-2).
Her older sibling Venus beat Romania's SimonaHalep in the first round for the second tournament in a row, and the 1999 Rome champion will take on Russia's Ekaterina Makarova as she seeks to improve on her second-round defeat on the blue clay last week.