Driving wind and rain meant it took 16 minutes for the first flash of quality to arrive as former Hibs midfielder Russell Latapy carved open his old team with an inch-perfect pass and Steve Thomson forced Simon Brown to make a spectacular save.
From Latapy's corner, recent Bairns signing Jean-Francois Lecsinel headed wide but Falkirk kept pushing and only a foul on Brown rescued the Hibs defence at another corner kick.
Sensibly, considering the difficult conditions, Falkirk kept things simple and from a long ball striker Daniel McBreen beat Scotland defender Gary Caldwell in the air but headed just wide.
The visitors improved after half-time with Garry O'Connor introduced up front yet Falkirk almost made the breakthrough when McBreen and Alan Gow set up Thomson for a wild shot over the top. Brown also made crucial saves from Stephen O'Donnell and Kenny Milne.
Having taken nearly 70 minutes to get an effort on target Hibs dominated the closing stages and, after being a virtual spectator for most of the game, home goalkeeper Allan Ferguson made terrific saves from Derek Riordan and, in injury time, Steven Fletcher.
Ferguson was finally beaten by a right-foot drive from O'Connor but the crossbar rescued Falkirk.