Raith created the better chances with Todd Lumsden and Paul McManus heading wide in the first half.
Peterhead were forced to reshuffle their line up with players out injured and they were restricted to long-range efforts, their best from a Douglas Cameron free-kick which was well saved by young Rovers keeper Stuart Hall.
Lumsden almost scored a spectacular own goal midway through the second half, sending a header from a Bobby Linn cross towards the goal only for the shot to be held by Hall.
Near the end Peterhead almost snatched the winner when substitute Martin Bavidge bore in on goal only to see his shot saved by the outstretched leg of Hall.