The home side were left clinging on in the second half as Hibs threw everything at them but they held on for an important win.
Hibs started brightly and there were early claims for a penalty when Jack Ross appeared to catch Scott Brown but referee Charlie Richmond was not interested.
Abdessalam Benjelloun then created a chance for himself but swiped his shot well over the top.
Falkirk took the lead after 14 minutes when the unfortunate Shelton Martis diverted a cross from Liam Craig past his own goalkeeper Zibi Malkowski.
It was the defender's third own goal of the season and Hibs should have levelled it moments later.
Brown cut the ball back into the path of Benjelloun but he lashed his shot against the top of the crossbar and over.
Falkirk took full advantage of the let-off. Meroune Zemmama was robbed 35 yards out by Craig and he raced ten yards before tucking a left-foot shot into the bottom corner of the net.
Steven Fletcher should have pulled a goal back when Zemmama sent him clear, but his shot was blocked by Scott Higgins and his follow-up effort was woeful.
Rob Brown sent a header wide as Hibs tried everything to get a goal back before half-time.
But Craig almost snatched a third in the final seconds after sub Guillaume Beuzelin gave the ball to him but his 25-yard shot was just too high.
Higgins did well to push a David Murphy free-kick past his post early in the second half as Hibs sought a way back.
Fletcher gave them it in 56 minutes when he turned the ball home from close-in after a flowing move ended with Benjelloun supplying the final pass.
Anthony Stokes came close to restoring Falkirk's two-goal advantage when Brown gave away possession but pulled his shot just inches past of the post.
Alan Gow wasted a better chance when Stokes put him through with a back-heel, but his hurried shot brushed the side-netting.
Hibs stormed the Falkirk goal after that but the home side survived.