Albion hit back for a point as these inseparable sides drew for the fourth time in 2004.
The Blues stay top and Morton's defeat at Brechin has boosted their promotion hopes, even though City are now just a point off the lead.
A competitive clash on a miserable afternoon was lit up by David Graham's wonderful goal just before the hour mark.
The Stranraer striker picked up the ball at the halfway line, spinning past Paul Nugent then evading Mark McNally before easily beating keeper Myles Hogarth with a cool finish for his 12th league goal of the season.
The visitors should have killed the game off but John Fraser glanced a header just wide from Kevin Finlayson's cross then Graham hooked the ball over the top following a corner.
Stirling were the stronger team in the first half and Connor Gethins should have done better than head over the bar after just 40 seconds, but their reward came with 11 minutes left.
Substitute Martin Glancy saw his fierce drive from the left corner of the box touched on to the underside of the bar by Andy McCondichie but Paul Hay was on hand to head home the rebound.
Dougie Wilson might have won it in injury time but his lob was tipped over by McCondichie and, in any case, Stranraer deserved their point.