Falkirk are one of only two teams to have beaten Hibs at home this season, but went into this game on the back of seven straight defeats and from the moment Dean Holden was sent off defeat number eight looked certain.
The signs were ominous for the visitors in the opening minute when Scott Brown's cut-back was blasted wide by Merouane Zemmama, but Falkirk dug in and ex-Easter Road favourite Russell Latapy tested returning keeper Andrew McNeil with a sizzling free-kick.
Jack Ross then cleared a weak effort from Steven Whittaker off the goal-line and at the other end, Stephen O' Donnell narrowly failed to reach Pedro Moutinho's cross and Latapy shot wide after timing his run perfectly from midfield.
Referee Craig Thomson ruled in Falkirk's favour when he booked Abdessalam Benjelloun for diving, rather than awarding a penalty, but his next major decision saw the Bairns reduced to ten men when Holden went in recklessly on Zemmama.
Hibs immediately pushed forward and Kasper Schmeichel had to make a stunning reflex save to keep out Brown's header on the stroke of half-time.
Benjelloun's fierce right-foot drive put Hibs in front early in the second period, although Falkirk were always dangerous and twice went close through headers from Kenny Milne and Darren Barr.
Benjelloun put the result beyond doubt 16 minutes from time with a slide-rule angled finish from Michael Stewart's pass.