It was Queens who started the brighter of both sides, and Chris Duggan went close on 15 minutes when he dragged his 30-yard drive just wide of the post.
McAllister then opened the scoring against the run of play two minutes later after bending a free kick around the Spiders' wall as Peterhead drew first blood.
The pendulum swung in favour of Peterhead once more when McIntosh smashed past Wullie Muir just before the half-hour mark to earn a slender half-time lead.
Peterhead looked determined to shut the door on Queens early in the second period and Muir kept out McAllister, who then drove just wide on the hour mark.
They looked on course for the final, although Jamie McKernon - who received a straight red card in the dying moments - had hearts in mouths late on when his 25-yard smash drifted agonisingly wide, but the Blue Toon held on.
Peterhead will meet either Rangers or St Mirren in the final.