Although this was unlikely to happen, they pushed for goals from the start of the game and were rewarded for their efforts in the 21st minute when Iain Diack headed home a Paul McGrillen cross.
Hopes were raised even further four minutes later when John McKeown fired a Diack knock-down past Mark Quinn to make it 2-0.
Throughout the game they looked vulnerable at the back, however, and Albion Rovers reduced the margin when Graham McGhee's free-kick from the edge of the box was deflected past Chris Fahey.
This seemed to deflate the Warriors, and after the resumption Rovers looked more likely to score with Fahey denying Craig Young with a superb stop and Craig Menzies also clearing an effort off the line.
Stenhousemuir extended their lead in the 73rd minute from the penalty spot through McGrillen after Diack had been upended by Quinn.
Rovers, to their credit, never gave up and Young scored the best goal of the game when he thundered the ball home from the edge of the box.
They could have equalised before the end of the match, but Stenhousemuir's John-Paul McBride tucked a free-kick into the net with the final kick of the game.