Barthel ousted second-seeded Anabel Medina Garrigues in the second round and next will meet fellow German Angelique Kerber, who advanced with a 6-0, 3-6, 7-5 win over Romania's Sorana-Mihaela Cirstea.
Kerber finished with a year-end No. 32 ranking after reaching the U.S. Open semifinals.
Peer advanced when Anna Chakvetadze had to retire from their semifinal in the third set because of cramping. Chakvetadze won the first set 6-4, but lost the second 6-4 and needed treatment at the break. She quit when she was down 1-0 in the third.