The Bairns held the upper hand throughout in Saturday's SPL clash and took the lead with a header from skipper Darren Barr after 68 minutes.
However, with veteran Latapy left on the bench, Nish popped up to nod in with eight minutes remaining after Rob Jones had out-jumped home keeper Scott Flinders at Alan O'Brien's corner.
The match was chosen by the home side to honour the veteran Trinidad and Tobago legend, who also played for Hibs, but the 40-year-old had to content himself with a place among the home side's substitutes throughout.
With last weekend's 2-1 defeat away to Hearts bringing an end to a six-game unbeaten run, Bairns manager John Hughes made only two changes.
In came Jackie McNamara and Dean Holden in the two full-back positions after ankle injuries kept them out at Tynecastle, with Dermot McCaffrey dropping down to the bench and Chris Mitchell losing out completely.
The visitors' team selection was easy enough for manager Mixu Paatelainen following last weekend's impressive 4-1 win over Motherwell at Fir Park but his unchanged line-up failed to hit the heights of that performance.
The presentation to Latapy before kick-off was quickly forgotten as the sides battled for early supremacy amidst icy cold conditions.
And it was Falkirk who immediately gained the upper hand with a strong-looking midfield quartet securing a stranglehold on possession.
Burton O'Brien fashioned the game's first opportunity after only six minutes as he took on David Van Zanten on the edge of the box but his shot scraped wide and hit the side netting.
Hibs looked content to sit deep and hit their hosts on the break and they almost did so to devastating effect in the 15th minute but Dean Shiels sent his shot wide after Darren Barr had blocked Steven Fletcher's attack.
Hibs keeper Yves Ma-Kalambay then intervened twice to ensure his team stayed level in the 20th minute, first turning O'Brien's free-kick round the post and then grabbing Michael Higdon's header acrobatically.
With Fletcher and Derek Riordan up front, Hibs were always likely to threaten and it was the former who was denied twice in quick succession just short of the half-hour mark.
First, his curling 25-yard free-kick was clawed away from the top corner by Flinders and then an acrobatic attempt at a volley was blocked by Barr 14 yards out.
Falkirk regained the bulk of possession as the interval approached and Higdon was only inches away from connecting with a flick-on from strike partner Steve Lovell on the apex of the six-yard box.
Hibs launched another quick counter-attack in the 60th minute but Lee Bullen prevented Riordan from turning a loose ball past Flinders.
The striker's subsequent corner had Flinders flapping but Sol Bamba's header scooped over the bar.
Two minutes later, the visiting fans were up out of their seats to proclaim what they thought was going to be the opening goal but Fletcher somehow screwed his header wide from only two yards out.
And just as Hibs looked to be threatening more, Falkirk took the lead.
O'Brien's cross looped over Ma-Kalambay and was met by Barr's header from an acute angle at the back post.
Falkirk's lead lasted only 14 minutes, however, as Hibs equalised with eight minutes remaining.
Alan O'Brien's corner looked easy for Flinders but the home keeper was outjumped by Easter Road skipper Rob Jones and substitute Colin Nish nodded in from close range.
As both teams searched for a late winner, Ma-Kalambay earned the visitors a point as he stretched to turn a deflection from defender Chris Hogg round the post.