Darren McGregor gave the visitors the lead but Falkirk hit back almost straight away through a header from Rory Loy.
Peter Houston’s side move up to fourth after a result that extended their unbeaten run to nine matches, although they will feel they could have secured all three points after having the best of the chances.
Rangers stay third in the table, with the disappointing draw meaning they reduce the gap to Hibernian to just one point.
Falkirk made a bright start in the early minutes, with Loy flashing in a tantalising early cross that only just evaded a cluster of players in the six-yard box before John Baird had an effort well blocked by McGregor after he had been played in by Mark Kerr.
It was the visitors, though, who took the lead on 20 minutes. Nicky Law delivered a deep free kick from only a few yards inside Falkirk’s half and Kris Boyd’s flick-on found McGregor after the home defence failed to clear.
The goal had come against the run of play and the hosts wasted little time by replying just two minutes later.
Craig Sibbald found Baird down the left and the experienced attacker whipped in an excellent cross to his strike-partner Loy, who escaped the attentions of Bilel Mohsni to divert a precise header inside the far post.
The Rangers defence was struggling to get to grips with Falkirk’s quick movement in attack and another last-ditch McGregor intervention was required to deny Sibbald after he had turned neatly in the box.
Will Vaulks was only just off target with a long-range strike, while Haris Vuckic’s tame finish after a swift counter-attack was the closest Kenny McDowall’s side came to restoring their lead prior to half-time.
The game was more even after the break, but clear chances were few and far between, with Rangers’ final ball letting them down on a number of occasions.
At the other end, Luke Leahy shot narrowly over the bar and Baird forced Lee Robinson into a low save with a strike from the edge of the box.
The visitors brought on Kenny Miller and David Templeton with 15 minutes remaining in an attempt to find a second goal.
Templeton was immediately involved, drawing a foul from Kerr at the edge of the area. Boyd, who was captain on the night in the absence of the injured Lee McCulloch, fired a powerful strike wide of the far post from the resulting free-kick in what would prove to be the last key chance of the contest.