Todd Lumsden's side are four points adrift of the Blues and eighth-placed Ayr United following their 5-1 hammering against runaway league leaders Queen of the South, writes Chris Jack.
Chris Aitken fired Stranraer ahead and Ryan Borris netted to double their advantage after just 20 minutes.
Steven Howarth pulled one back for Rovers just after the break but Aitken struck again to complete his double, firing home from the penalty spot with four minutes remaining.
Tony Stevenson ensured a dramatic finish, scoring with a free kick just seconds later.
But it was only a consolation for Rovers who suffered a disappointing start to the new year.
In the Third Division, Queen's Park bounced back from their late Rangers heartache with a 4-1 win home over Clyde.
Gardner Speirs' side suffered an agonising derby defeat against the Gers but got back to winning wins in impressive fashion as they continued their dominant recent run against the Bully Wee with a ninth consecutive triumph over their visitors.
Michael Keenan got the Spiders off to the perfect start, scoring inside the opening two minutes.
And when Sean Burns converted soon after, the hosts were well on course for victory.
Despite Kevin Watt pulling Clyde back into the game, a Pat Scullion own goal and Keenan's second of the afternoon condemned Jim Duffy's side to defeat.