The American immediately dropped her serve on Centre Court as Peer made a strong start but the 18th seed was left gasping for air as Williams blasted her way to the opening set in under half an hour.
Peer made up for an early break in the second but it proved too big an effort as she conceded the last three games, the final one to love on her own serve after one hour and seven minutes.
Next in line for Williams will be Australian seventh seed Samantha Stosur, who knocked out four-times champion Justine Henin on Court Suzanne Lenglen.
Asked whether she was surprised by the result, Serena reminded everyine the Australian was a semi-finalist here last year.
“You can never underestimate anyone, and Sam is actually a wonderful claycourt player,” she told reporters.
“I think she proved that last year, and this year I think she has only lost twice on the clay. So she is someone you cannot overlook. She has a good chance to go all the way.”
Serena, however, stands in Stosur’s way as she bids for a second title in Paris after her 2002 title.
“This year my game is better, I hope I am going to win. I live here, I love Paris, it’s a wonderful city,” the 2002 champion told a stunned crowd as she responded to a courtside interview in French.
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