Match ends, Falkirk 1, Rangers 3.
An element of patience was required before Rangers secured their passage to the quarter-finals of the Scottish League Cup.
A set-back had to be overcome, since Falkirk opened the scoring after just five minutes through Rory Loy.
It took only three minutes for the visitors to respond, through an Owain Tudur Jones own goal.
And in the final quarter of the game Dean Shiels and Ian Black established a lead for Ally McCoist's side.
Falkirk were never overwhelmed, but Rangers earned the victory by showing greater quality in the final third.
A frantic start to the game seemed to catch both sides unawares.
The openness of the play was stirring for spectators, who saw two goals in the space of three minutes and began to anticipate a thrilling encounter, but it was galling for the two managers since their careful strategising appeared to have been in vain.
The Falkirk defenders were certainly alarmed when a simple through ball sent Shiels bearing down on goal, only for the striker to lose his footing and goalkeeper Jamie MacDonald to take control of the situation.
Vulnerability was not uncommon, though, and Bilel Mohsni was lax moments later, failing to deal with a high ball and gifting possession to Falkirk.
Blair Alston needed little encouragement to be bold and his shot from the edge of the area was fiercely struck.
Steve Simonsen was able to block, but the ball spilled out for former Rangers forward Rory Loy to convert from close range.
There would have been a surge of optimism amongst the home players, but it was swiftly quelled.
Only three minutes later, Stevie Smith surged down the left and his whipped cross was turned past MacDonald by the unfortunate Tudur Jones, who was stretching out a leg to try to block the ball.
It was a reprieve for Rangers, but also a testament to their resolve. Long-range efforts from Black and Smith soon followed, with the ball spinning just wide of the upright on both occasions.
Command of the game was beyond the ability of both sides. Scrappiness became a feature, with referee Alan Muir having to be stern in ticking players off in order to maintain control.
The slickness of the surface - which had been watered beforehand and then subjected to a heavy downfall - did not help either side, although Mohsni was particularly prone to erratic behaviour.
The defender took time out from slicing passes astray to slip at an inopportune moment, allowing Joe Shaughnessy to burst into the penalty area.
The full-back was challenged, but the ball broke to Tom Taiwo and his shot curled just wide of the far post.
The creative players were generally marginalised, though, by the nature of the game as much as the conditions underfoot.
No composure could be imposed on Mohsni during the interval, and his first involvement of the second half was to fail to deal with a straightforward piece of defending.
Having presented the ball to Loy, the defender had to watch helplessly as a cross reached Alston and the Falkirk player's shot was turned away by Simonsen.
As the pace of the game slowed, Rangers brought on David Templeton for Aird, who had been uninvolved. The intention would have been to try to introduce a spark of invention, but the second goal when it came was simple in nature.
A ball through the heart of the home defence sent Shiels scampering through and his shot was firm enough to still fly high into the roof of the net despite a valiant attempt to push it clear by MacDonald.
Rangers have not always exerted control over opponents this season, so no lead could be considered wholly secure.
Peter Houston's team were always capable of being sprightly and in Craig Sibbald they had a player who carried a threat from set pieces. The midfielder delivered one free-kick that Will Vaulks headed at Simonsen, then another drew a direct save from the goalkeeper.
If there was a measure of the narrow distance between the two sides it was that the slightly better chances came to Rangers.
One Smith cross, for instance, was headed powerfully downwards by substitute Jon Daly, prompting an impressive flying save from MacDonald.
The goalkeeper was no match for Black's measured, sipping and curling shot in the final moments, though, with the ball dipping over his reach and into the top corner.
That attack followed an unsuccessful appeal for handball against Mohsni in the Rangers penalty area as Falkirk's tournament ended at the third-round stage.
Falkirk manager Peter Houston: "I felt were denied a stonewall penalty kick. Rory has taken a bad touch but it has smacked up off the boy's arm and the players are adamant it was a penalty.
"I have no idea why the referee didn't give it. The rule is if your arm is up in the box you and it hits it, then it's a penalty kick. Unfortunately, the referee never saw it the way I saw it."
Rangers manager Ally McCoist: "There's no doubt it hit his hand but deliberate handball? Not for me. I'll watch it again and stand corrected if need be but I didn't think it was deliberate.
"Dean Shiels is different in very few players can play in the hole and link up when you go 4-4-1-1. Shiels is ideally suited to do that.
"We've got a lot of direct frontmen whether it's Kris Boyd, Kenny Miller, Jon Daly or Nicky Clark. If you're looking for someone to drop off into that hole Dean is perfect to do that.
"He scores goals too. Look at his record. He was out injured for a period last season but he scores. Anyone who does that will have a future here."
- 15DickSubstituted forCooperat 80'minutes
- 34Tudur-JonesSubstituted forBia Biat 69'minutes
- 7TaiwoBooked at 68minsSubstituted forDurojaiyeat 76'minutesBooked at 87mins
- 33LoyBooked at 48mins
- 28Bia Bi
- 5WallaceBooked at 24mins
- 3MohsniBooked at 83mins
- 4AirdSubstituted forTempletonat 56'minutes
- 22ShielsSubstituted forHardieat 86'minutes
- 15BoydSubstituted forDalyat 78'minutesBooked at 90mins
- Alan Muir
- Shots on Target
Second Half ends, Falkirk 1, Rangers 3.
Jon Daly (Rangers) is shown the yellow card.
Blair Alston (Falkirk) wins a free kick on the left wing.
Foul by Jon Daly (Rangers).
Corner, Falkirk. Conceded by Steve Simonsen.
Attempt saved. Alex Cooper (Falkirk) right footed shot from outside the box is saved in the top right corner.
Joe Shaughnessy (Falkirk) wins a free kick in the attacking half.
Foul by Lee Wallace (Rangers).
Goal! Falkirk 1, Rangers 3. Ian Black (Rangers) right footed shot from outside the box to the top right corner. Assisted by David Templeton.
Attempt saved. Rory Loy (Falkirk) right footed shot from outside the box is saved in the bottom right corner.
Corner, Rangers. Conceded by Jamie MacDonald.
Attempt saved. Jon Daly (Rangers) header from the centre of the box is saved in the top right corner.
Attempt saved. Steven Smith (Rangers) left footed shot from outside the box is saved in the centre of the goal.
Olumide Durojaiye (Falkirk) is shown the yellow card.
Foul by Olumide Durojaiye (Falkirk).
Ian Black (Rangers) wins a free kick in the defensive half.
Substitution, Rangers. Ryan Hardie replaces Dean Shiels.
Foul by Craig Sibbald (Falkirk).
Ian Black (Rangers) wins a free kick in the defensive half.