Kris Boyd put the home team ahead with his 21st goal of the season, but when Carl Finnigan equalised with his first goal for Falkirk, it looked as though Rangers would have to settle for a share of the points.
However, skipper Barry Ferguson stepped in to force the ball home from close range after an intelligent free-kick from Charlie Adam.
To add to Falkirk's woes they also saw Thomas Scobbie ordered off near the end for a crude challenge on substitute Chris Burke.
Rangers were first to threaten when Nacho Novo's pass found Ferguson but Kasper Schmeichel raced from his line to block the shot.
Falkirk kept possession well but lacked any cutting edge before falling behind to a clinical finish by Boyd.
The striker had rarely been seen before he chested down Alan Hutton's deep cross and shot low past the keeper.
The visitors were more adventurous in the second half and early on Allan McGregor did well to parry Finnigan's snap-shot.
Rangers should have added to their lead after a swift break but Schmeichel blocked Ferguson's effort and Novo's shot was cleared off the line.
The Bairns equalised when, from a suspiciously offside position, Finnigan shot low past McGregor.
Schmeichel was then forced to once again save well from Novo. Adam then played a quick free-kick to Ferguson and, from his cross, Novo's effort at the back post was blocked by the keeper.
However, he could do nothing to prevent Ferguson knocking the ball home at the back post.