Buddies midfielder Patrick Cregg cracked a shot against the post early in the first half but that was as close as the Scottish Premier League side came to scoring in a frustrating afternoon for them at New St Mirren Park.
Danny Lennon's side dominated for most of the match but the part-timers defended with dogged resilience.
The Buddies simply ran out of ideas and were met with a chorus of boos from their angry supporters at the final whistle and neither they, nor the St Mirren players, will look forward to the trip north.
Lennon gave a debut to midfielder Jim Goodwin, his new arrival from Hamilton as skipper John Potter returned from suspension to take his place in the Saints defence.
St Mirren dominated possession in the first half but for the most part huffed and puffed.
Cregg had several efforts on goal of various quality but came closest in the 13th minute after being set up somewhat fortuitously by Paisley striker Craig Dargo at the edge of the penalty area.
The Irishman crashed a shot off the base of Jon Bateman's right-hand post, with David Donald clearing for a corner, which came to nothing.
As the snow began to fall, any St Mirren hopes of an easy afternoon appeared to cool as Peterhead refused to buckle despite having to reshuffle their side twice before the interval.
Moments after St Buddies midfielder Jure Travner headed a Goodwin cross past the post from six yards, the visitors had to replace the injured Mann with Callum MacDonald.
The home side continued to be wasteful with defender Darren McGregor heading a Cregg free-kick over the bar from only six yards just before the half-hour mark.
Bateman then made a decent save down at his left-hand post from Paul McGowan's header at the expense of a corner after the impressive Goodwin swung a cross in from the left but again the Paisley side could not capitalise on the set-piece.
Two minutes from the break Peterhead had to make another change after Scott Ross blocked a McGregor shot, with the visiting defender carried off on a stretcher to be replaced by Paul Emslie.
David van Zanten replaced the injured Marc McAusland for the start of the second half and, although the Paisley side continued to dominate, the goal looked no more likely to arrive.
In the 51st minute midfielder Steven Thomson had a decent drive from 30 yards but it sped straight in to the arms of Bateman.
Lennon made his second change moments later when striker Gareth Wardlaw came on for the ineffective Michael Higdon but it was McGowan who blazed over from just inside the box after Bateman had punched a Cregg cross straight to his feet.
In the 66th minute, as Peterhead were caught up the park for the first time, Travner broke down the left and cut in before curling a right-footed shot just past the far post, moments before Thomson sent a long-range drive wide.
As the nerves among the home fans began to affect the St Mirren players, the visitors sensed they could perhaps go one better than a replay.
In the first minute of stoppage time though, after van Zanten threw in a cross from the right, Bateman made a fine fingertip save from Dargo's header and again the visitors defended the corner comfortably to earn a well-deserved replay.