Jamie McKernon opened the scoring with a penalty after Ross Fisher had fouled Paul Woods.
Vincent Berry made it 2-0 from David Galt's cross and Woods fired in the third just before half-time.
The Spiders, who move up to fourth, could have added to their treble, while Shire struggled to create chances.
Queen's Park boosted their League Two play-off push with victory over Scottish League Two basement club East Stirlingshire.