In a pulsating end-to-end encounter City started the better side with Shane Sutherland coming close with a long range effort that scraped the top of the bar. They were close again through a Craig Gunn effort that flew just inches wide while Mark Nicolson sent a header just over the top from the resulting corner kick.
It was not all City by any means, an Andy Rodgers effort going close for Peterhead - but Elgin had the upper hand so it was no surprise when they took the lead. Another well delivered corner kick found the head of Nicolson and this time he sent a header back along the danger area - where David Niven was on hand to send the ball into the roof of the net.
McAllister should perhaps have equalised for the home side when he was left in the clear but he failed to connect with Redman’s cross.
City goalkeeper Ray Jellema, freed to play the game courtesy of an appeal against his red card on Saturday, proved his worth with a great save from McAllister as the home side sought an equaliser before the interval.
It was, however, Elgin who came closest to adding to the scoring early in the second half. A superb cross from Gunn located Shane Sutherland in space but his goal-bound header was superbly blocked by goalkeeper Smith.
City were next denied a penalty kick when Wyness went over in the area - but only earned a yellow card for his troubles, referee Northcroft decided he had attempted to deceive.
Another stunning save from Smith again defied the visitors a second goal, this time from Harkins who had charged through the home defence and into the penalty area before unleashing a great effort on goal.
Just after the hour mark Elgin were made to pay for missing these opportunities, a shot from Sharp taking a wicked deflection and ending up in the back of the City net.
The game raged on through the final half hour with both sides having chances - but the final say belonged to Peterhead. Rodgers went on one final surging run down the flank in the last minute of the game, cutting back for Redman to get ahead of his marker and poke the ball into the net.
Full Time: Peterhead 2 Elgin City 1
Elgin City: Jellema, Niven, McMullan, Crighton, Duff, Nicolson, Gunn, Harkins, Wyness, Sutherland, Urquhart. Subs: Black, McKenzie, Beveridge, McLeod, McKinnon, McAulay.
Referee: Matt Northcroft
Match Highlights - https://vimeo.com/83276921 (Elgin City TV not present at this game)