"I'm here to win every match that I play. That's basically what it is, you know. Nothing more or less than that," said the American.
Venus and Peer have a history. When the Israel player was denied a visa to play in the United Arab Emirates in 2009 on 'security concerns', Venus Williams spoke in her support.
However, when they meet on court, Venus shows no signs of the off-court empathy.
Venus and Peer have crossed path six times on the court and all were clinched by the American in straight sets. Four of these encounters happened in 2010.
"Every time I played Venus, I had (a) tough time, and she was always kind of killing me. So today was much closer," Peer said after putting up a real stiff fight.
30-year-old Venus, who was found tugging on her pink minidress several times during the match, had sister Serena Williams cheering her on from the stands.
Younger of the sisters, Serena (28), who denied Venus one of the US Open titles in the past, made headlines with her clingy animal print dress.
Serena was forced to pull out off the 2010 tournament due to an injury.