The visitors were on top from the start and Phil Reid forced a smart stop from John McCafferty after 16 minutes.
Craig Higgins came even closer after 28 minutes but his header was cleared off the line by Fife defender Craig Lumsden.
East Fife were struggling to capture their scoring form from midweek when they put six past Albion Rovers.
Their hat-trick hero that night, Sean Paliczka, almost put his team in front but Kieron Renton pushed a shot around the post.
Reid missed a golden chance for Elgin after 32 minutes when a he defensive slip left him a clear run on goal, but he over-ran the ball and wasted the chance.
Stephen Tarditi almost brought a dull game to life when he smacked a shot off the post.
Hugh Dickson then stole into the box and should have done much better than head Adam Nelson's cross over the bar.
A deflected free-kick after 68 minutes almost gave Elgin the lead, but keeper McCafferty got a hand to the ball to make the save.
Greig McDonald finally broke the deadlock after 75 minutes when Elgin couldn't clear the ball and he hammered home from the edge of the box.
Martin Harty missed a great chance to equalise after 82 minutes and the game was lost when Johnny Mitchell scrambled in a second goal for East Fife with three minutes remaining.