Albion were thumped 6-0 at home last time the teams met and looked hell-bent on revenge from the first minute when 17-year-old Ian Douglas scored.
He chased a long punt, muscled past the hesitant defenders and confidently stroked an angled shot past keeper John Dodds.
The little hitman almost did it again after six minutes, but Dodds raced off his line and grabbed the ball before clattering Douglas to the ground.
East Fife levelled a minute later when Chris Fahey couldn't hold John Ferguson's fierce strike and Jonathan Mitchell pounced on the rebound.
Albion's Jered Stirling tested the keeper with a low free-kick and Douglas came close again with an effort that shaved the post. East Fife's Gary Kelly was lucky not to get booked after an ugly two-footed lunge on Douglas. John Bradford should have punished them from the resultant free-kick, but his header carried no power.
Rovers were denied an excellent goal on the hour when Dodds finger-tipped James Mercer's header over the bar.
Mitchell was close to putting the Fifers ahead with a smart turn and shot after 67 minutes, while Craig Lumsden sent a tame shot into the keeper's arms shortly after.
Mercer picked up a second yellow card with just seven minutes left, and substitute Leslie Byle thought he'd given Fife the winner with a piledriver that whistled wide.
Beith should have won it with just seconds left, but from just 4 yards out he sent his headre sailing over the bar.