It was no more than Falkirk deserved for an enterprising display but Hibs finished the game with ten men after Thierry Gathuessi was sent off in stoppage time for his second bookable offence. Hibs had earlier led from a controversial 21st minute penalty by Clayton Donaldson.
Hibs started well and Tim Krul was forced to beat out a shot from Steven Fletcher only for Filipe Morais to head the loose ball tamely into the keeper's arms from ten yards.
There was a let-off for Hibs at the other end when Gathuessi gave the ball to Scott Arfield in the area but the midfielder could not direct his shot on target.
Rob Jones was then woefully short with a back-pass but Pedro Moutinho's shot only found the side-netting.
Moutinho was prepared to try his luck from distance and McNeil did well to clutch and hold a low shot from the striker which bounced wickedly up off the turf.
Hibs nosed in front after 21 minutes. Dean Holden made a rash challenge on Gathuessi in the area but referee Brines indicated that the defender had played the ball.
However, the linesman flagged for the spot-kick and Mr Brines changed his mind much to Falkirk's anger.
Donaldson calmly sent Krul the wrong way as he slid the penalty into the corner of the net to put Hibs ahead.
But there was an immediate setback for Hibs when Fletcher went off with an injury which he picked up after a challenge from Tom Scobbie in the build-up to the goal.
Falkirk almost equalised moments later but Barrett could not get on the end of Michael Higdon's shot across the face of goal.
The Bairns were then caught short-handed at the back during Hibs' next raid as Donaldson played in Lewis Stevenson but his shot struck the top of the crossbar.
McNeil produced a terrific one-handed save to keep out a ten-yard shot from Higdon from Moutinho's corner.
Arfield should haved score late in the half but lofted his shot over with just McNeil to beat.
The second half did not live up to what had gone before half-time but Falkirk did not care as Barrett produced a wonderful effort to equalise ten minutes from time.