The first 20 minutes saw a quiet start with Stenhousemuir's Iain Diack coming close to a goal by getting on the end of an inswinging corner only to see his looping header cleared off the line by City's David Hind.
In the 20th minute Martin Charlesworth got on the end of a throughball from Martin Johnston only to send his shot screaming over the Stenhousemuir crossbar.
After a sustained period of Elgin pressure the breakthrough finally came 33 minutes into the first half as Adam Moffat's strike from 20 yards flew into the top right-hand corner of the Stenhousemuir net.
John-Paul McBride chipped the City defence in the 41st minute to leave Diack one-on-one with Elgin keeper Kieron Renton who stayed on his feet and comfortably kept City's lead.
In the 54th minute Elgin moved 2-0 up courtesy of an own goal by Mark Cowan who headed a Steven Mackay corner into the back of his own net.
City continued to attack and almost scored a third when Charlesworth waltzed past the Stenhousemuir keeper and squared the ball only for it to be cleared by Andrew Gow.
That did not spoil the home team's spirit though as Borough Briggs erupted when the final whistle blew as Elgin sealed their second League victory in three games.