Trailing at half-time to a fantastic Derek Riordan double, Falkirk looked dead and buried but an energetic second-half showing brought them the points.
Hibs were in front after only 40 seconds when Riordan cracked in a left-foot volley from 20 yards to leave Matt Glennon helpless.
And although the home side had the majority of the play they lacked a killer touch and tended to over-elaborate.
Riordan came close again from an unlikely angle but Falkirk also had their chances with Alan Gow glancing a header wide.
After Gary Caldwell saw his header cleared off the line by Stephen O'Donnell Hibs increased their lead after 32 minutes.
And again, it was down to the glorious ball striking talent of Riordan who curled a perfect free-kick round the wall and into the back of the net from 25 yards.
However, Falkirk gave notice of their battling qualities and Darryl Duffy missed a good opportunity before bringing a fine save from Zbigniew Malkowski with a powerful 25-yard drive.
Falkirk needed to get a goal back early in the second half and it came after 48 minutes when Duffy pulled down O'Donnell's driven pass and slipped the ball past Malkowski.
And with Hibs' defence at sixes and sevens Falkirk were level eight minutes later when Duffy played in Gow who held off Hogg to slide the ball under the advancing keeper.
Hibs enjoyed a period of greater possession and Kevin Thomson and Stephen Whittaker both went close from long range.
But it was Falkirk's day and they plundered the points with a bizarre winner.
Kenny Milne's cross was punched by Malkowski but the ball bounced off Duffy and into the empty net.