Rory McAllister's fine free-kick put Peterhead in front before Paul Woods' penalty levelled things midway through the first half.
McIntosh smashed home what would prove to be the winner five minutes later.
Jamie McKernon was sent off late on as Peterhead set up a final against either Rangers or St Mirren.
McAllister opened the scoring on 17 minutes when he curled a free-kick into the bottom corner.
Woods was given the chance to regain parity for Queen's just five minutes later when McIntosh brought down Sean Burns in the penalty area. The midfielder slotted home the spot-kick to notch his seventh goal of the season.
McIntosh redeemed himself on 27 minutes when he tapped home Kevin Dzierzawski's free-kick for the decisive goal.
The Spiders lost McKernon to a red card at the end of the game as Peterhead held on to make the first final in their 124-year history.
Leighton McIntosh's goal proved decisive as Peterhead beat Queen's Park to reach their first ever senior cup final in the Petrofac Training Cup.