The visitors trailed following Alistair Love's close-range finish from Michael Dunlop's pass.
Rovers' Spas Georgiev was off target from a similar distance and Peterhead goalkeeper Graeme Smith denied Love and Andy Barrowman.
Scott Ross headed off target for the visitors but McAllister converted following Scott McBride's handball.
Rory McAllister's stoppage-time penalty secured a draw for Peterhead against Albion Rovers in Scottish League One.