Wickmayer, the third seed and world No 16, produced some strong serves and solid forehands on the way to an 86-minute victory over her 30th ranked opponent.
Peer fought hard throughout, but was hampered by six double faults, a number of them coming at crucial times of a contest played in windy conditions.
Wickmayer, who has yet to drop a set, will now meet the winner of the all-Italian clash between top seed Flavia Pennetta and No 4 seed Francesca Schiavone.