Serena and Venus also won their opening doubles match, beating Romania's Sorana Cirstea and Simona Halep 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 Simona Halep 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 Simona Halep 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 Simona Halep after the Romanian beat Russia's 24th seed Alisa Kleybanova 6-4 7-6 (7-2).
Her older sibling Venus beat Romania's Simona Halep 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.