Julia Goerges of Germany upset wild-card entry Stephens 6-3, 6-2, while Camila Giorgi of Italy overcame defending champion Cornet 6-4, 1-6, 6-3.
Goerges, a semifinalist at the Pattaya Open in Thailand in February, did not face a break point. She broke for a 5-3 lead in the first set. Stephens dropped serve in the first and seventh games of the final set.
Cornet beat Giorgi in the Katowice Open final last month in Poland. But the Italian got her revenge Tuesday despite making nine double faults.
The fourth-seeded Petkovic beat French wild-card entry Pauline Parmentier 6-3, 6-4, the seventh-seeded Peng defeated Australian qualifier Ashleigh Barty 7-5, 7-5, and Lucic-Baroni stunned sixth-seeded Bojana Jovanovski of Serbia 6-4, 6-0.
Petkovic led 5-0 in the opening set against Parmentier and 3-0 in the second. Lucic-Baroni offset seven double faults by saving all four break points she faced against Jovanovski.
McHale cruised past Alexandra Cadantu of Romania 6-1, 6-2, Davis dismissed Belarusian qualifier Olga Govortsova 6-2, 6-4, Puig edged Johanna Larsson of Sweden 7-5, 7-6 (5), and Soler-Espinosa beat Stefanie Voegele of Switzerland 6-0, 7-6 (5) for the first time in five matches.