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.
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).
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.