Falkirk had the better of much of the match and the visitors had Cammy Bell to thank for two crucial second-half saves to deny Alex Cooper and David McCracken when the scores were level.
Lewis Macleod then broke the deadlock in the 78th minute when his strike took a fortunate deflection off Will Vaulks to beat a helpless Jamie MacDonald in the home goal, while victory was sealed six minutes later when substitute Nicky Clark pounced from close-range.
Kris Boyd had a late strike ruled out for offside but it mattered little to the result as Rangers walked away with the three points.
Falkirk began the game on the front foot and were the first to threaten. Blair Alston exploited some early uncertainty in the visitors' backline to raid down the right and produce a dangerous delivery, which Tom Taiwo hooked wide at the far post under pressure from goalkeeper Bell.
The hosts came even closer moments later when Cooper crossed from the opposite side and Alston flicked an ambitious effort narrowly wide of the far post.
Rangers responded when David Templeton fired a powerful shot just off-target from 25 yards out after latching on to a partially cleared corner in what would prove to be their best attempt of the first half.
Disaster almost struck for the visitors when a loose header from Bilel Mohsni, who was returning from a two-game suspension, allowed Cooper through on goal, but the defender salvaged the situation with a last-ditch challenge.
The home side had looked the more likely team to score in the first 45 minutes and the second half started in similar fashion, with only two excellent saves by Bell preventing Falkirk from taking the lead.
After Connor McGrandles had been fouled by Mohsni on the edge of the area, Cooper's free-kick looked destined for the top corner until Bell dived to his left to produce a vital fingertip stop.
Cooper sent in the resulting corner for McCracken to head down from close range but the defender was thwarted by another impressive Bell save, with the keeper getting down quickly to parry.
Rangers finally created a clear opportunity when Lee Wallace's free-kick caused problems in the home defence, but Lee McCulloch could only fire over the crossbar after the ball bounced invitingly into his path.
At the other end, a quickly taken free-kick sent Rory Loy racing into the penalty area and his cut-back was inches away from finding a cluster of advancing Falkirk attackers.
The game began to open up as the second half progressed and Clark headed straight at Jamie MacDonald after Boyd had supplied the pass.
Just as the game appeared to be drifting towards a goalless draw, a surging run from substitute Fraser Aird found Macleod in space outside the area and the midfielder's shot took a wicked deflection off Vaulks and rolled past a stranded MacDonald into the far corner.
Buoyed by their opener, a second goal followed on 84 minutes. Macleod's corner was fired towards goal by Nicky Law and Clark helped the ball over the goal-line from close-range.
In a frantic finish, MacDonald twice denied Aird in a goalmouth scramble before Rangers had the ball in the net again when Boyd's effort was ruled out for offside after MacDonald had parried McCulloch's strike.