The Bairns also took their first points from a half-time losing position in more than 20 games with the tie at Westfield.
But despite the positive stats, Ray McKinnon's men still slipped to the bottom of the SPFL Championship table.
HOW IT HAPPENED: Falkirk 2 ICT 2 - Matchday Blog
Ian McShane's goal direct from a corner hauled back Caley who had taken the lead on the 45th minute thanks to Aaron Doran's top corner strike. Prior to that the sides had exchanged goals through Shaun Rooney and Zak Rudden.
Falkirk handed home debuts to seven players, and introduced another two off the bench to give them their Westfield bows. But though it was new characters in a similar storyline as they fell behind to a clever and sleekit free-kick routine in one of the opening chapters.
Expecting the 12th minute delivery from Joe Chalmers, one of four ex-Bairns in the Caley line-up, the deceptive ball was delivered low and tapped in by Shaun Rooney's foot and beyond new Bairns goalie Harry Burgoyne.
The on-loan Wolves man enjoyed a busy afternoon of some flamboyant saves, despite conceding twice and was one of the nine debutants.
Caley had the better of the opening exchanges, prompting the visiting fans to remind the Bairns of their success in the 2015 Scottish Cup Final - a far cry from the predicament Falkirk now find themselves in.
LEAGUE TABLE: Ladbrokes SPFL Championship
Burgoyne had to beat out an Aaron Doran effort and gather a close-range Nathan Austin header which the former Bairns man should have converted, unmarked and directly in front of goal.
It was a let-off and gratefully received by Falkirk who hit back.
Some of the build-up play was positive without being penetrative, until they sliced through the defence just before the half-hour mark and Mark Waddington rolled the ball across goal for Zak Rudden to tap in.
That buoyed the Bairns and the same duo almost converted a Ross MacLean cross two minutes later when Caley goalie Cameron MacKay flapped at the delivery but it was just too high for both.
The Bairns were in the ascendency and the home side were expectant with half-time approaching. But the wind was taken out of their sails by another set-piece from the visitors.
Liam Polworth's set-piece was headed out by Ciaran McKenna but returned with aplomb by Doran who smashed the ball into the top corner from the edge of the box for the half-time lead.
It was an ominous sign for the Bairns whose last 20 games have seen them trail at half-time in more than a quarter - and take nothing from them.
PLAYER PROFILE: Ciaran McKenna
With Partick Thistle leading at Firhill against Queen of the South, points became imperative, and although the Bairns applied significant pressure in the second half, the point came from an unlikely source.
Ian McShane took a corner in the south east section of the pitch, whipped the ball into the box, over Cameron MacKay and into the top corner of the net. The midfielder had hit the bar with a corner on his Bairns debut against Ayr - accidentally by his own admission - but this time it was gratefully received.
It came ten minutes after the interval and dispelled the notions that the end of the first half brought. The Bairns scrapped hard to maintain their position with the play-off hopeful Highlanders. Mark Waddington took it literally and tangled with Carl Tremarco on the right, and his eventual substitution brought frustration from the stands after a combative hard-working performance from the on-loan Stoke City man.
The battling Bairns could have won it late on with Zak Rudden scooping a great chance over and David Keillor Dunn having a strike blocked.
Caley too could have snatched the points when Ciaran McKenna's outstretched arm blocked a Darren MacCauley effort, but ref David Munro waved away the legitimate penalty claims, much to John Robertson's annoyance.
MATCH STATS: Falkirk 2 ICT 2
In the end the new-look Bairns extended their unbeaten run through January, and showed resilience to battle back from a goal down, twice, despite slipping down to the bottom of the table.