Peer ousted eighth-seeded Anna Tatishvili 6-1, 6-1. She won more than 60 percent of the points both serving and receiving.
Peer ended up with six breaks in seven games Tatishvili served. She saved seven break points in the first set and, while dropping serve once in the second, was 4-for-4 in break opportunities in finishing off the win.
She next faces Alexandra Cadantu, who was up 4-6, 6-5, 4-0 in her second-round match when Andrea Hlavackova retired. They had played nearly 2 1/2 hours.
No. 6-seeded Chanelle Scheepers came away a 7-5, 6-4 winner over Petra Martic by cashing in five of her 15 break chances. Danka Kovinic defeated Valeria Solovyeva 6-1, 3-6, 6-1 in the other second-round match. Scheepers and Kovinic are to square off in Friday's quarterfinals.
The quarterfinal matches determined Wednesday have third-seeded Simona Halep playing Timea Babos and No. 4-seeded Annika Beck going against Yvonne Meusburger.
Wisconsin business offering 'therapeutic cuddling' forced to close
Megyn Kelly: Santa Claus and Jesus are both white men