"It is my second final and second title, it was great a week and I'm happy for that," said Peer, who won her first tour singles title earlier this season at Pattaya City, Thailand.
"In the second set, I started to play more aggressive, tried to win the first few points and not to let (Stosur) move me around," she said.
It was the first-ever singles final for Stosur, who is a part of top-ranked doubles team on the WTA Tour.
The third-seeded Peer won $22,900.
It was the second meeting between the two players. Peer won both.