He reacted first in the six-yard box to nod the ball home to ruin all of Falkirk's good work.
Both sides had chances to win it in the closing stages but a draw was probably a fair enough result.
Falkirk settled first and Burton O'Brien was given too much time and space in the Hibs penalty box as he whipped a right-foot shot into the side-netting.
Rob Jones then lost his footing but recovered in time to hook the ball away from Steve Lovell with Hibs short at the back.
Hibs had a chance at the other end after Darren Barr had stifled Steven Fletcher but his low shot was always going wide.
Scott Flinders then looked none too convincing in dealing with a Derek Riordan volley but he grabbed the ball at the second attempt.
Lovell reacted angrily to a challenge by Rob Jones as the game boiled over but both players got away with a stiff lecture from referee Alan Muir.
O'Brien was on target from the resultant free-kick but Yves Makalamby managed to slap the ball past his right-hand post.
Makalamby then leapt theatrically to his left to clutch a glancing header from Michael Higdon with Hibs under the cosh.
But it was an evenly-balanced contest. Flinders did well to touch a free-kick from Fletcher past his post after Patrick Cregg had fouled Riordan.
Falkirk's passing was slicker than Hibs', but too often the final ball picked out an opposing defender than a home striker.
Hibs almost broke the deadlock after an hour when Flinders missed Riordan's corner but he bundled his shot over the top.
Fletcher then came close with a header at the back post from David Van Zanten's cross.
But it was Falkirk who took the lead after 68 minutes. Makalamby failed to deal with a deep cross from O'Brien and Barr nodded home a simple goal at the back post.
But just when it looked as if Hibs would hold on, Nish nodded an equaliser with eight minutes left after Jones had headed on an Alan O'Brien corner.
Makalamby then made two great saves late on to deny Falkirk. He tipped a long-range effort from Kevin McBride over his crossbar and then reacted well to keep out a shot that came off the boot of Chris Hogg.