Match ends, Falkirk 0, Rangers 2.
Two stoppage-time goals against 10-man Falkirk spared Rangers a Scottish Cup fourth-round replay.
It looked like the Bairns would live to fight another day despite David McCracken's dismissal after 57 minutes.
Rangers captain Lee McCulloch had the subsequent penalty kick saved by goalkeeper Michael McGovern.
But Nicky Law fired the opener from close range and substitute David Templeton slotted in the second to give Rangers a deserved victory.
And it not only took Rangers into the draw for Monday's fifth round draw but stretched the League One leaders' winning streak to 18 games.
It is not often that a team from a lower division starts as favourites, especially away from home, but that is the situation that has presented itself in the case of Rangers over the last two seasons.
They travelled to Falkirk Stadium having already beaten the youthful Bairns twice last season in both the League Cup and Ramsdens Cup - and that was before strengthening their squad after winning the Division Three title.
But Falkirk, sitting fourth in the Championship, could take heart from the 3-2 League Cup win in 2011, when the Ibrox outfit were even stronger prior to the club's financial collapse.
Both managers added experience to their side for this latest encounter, with Honduras international Arnold Peralta replacing Fraser Aird on the Rangers wing.
Experienced former Dundee United, Wycombe Wanderers and St Johnstone man McCracken came into Falkirk's defence at the expense of Jonathan Flynn.
And, while the sides were fairly even in terms of possession and territory during the first half, it was the home back four who were under the greater pressure.
McGovern saved bravely at the third or fourth attempt as the ball bobbled about a sea of legs inside the penalty box.
McCulloch sent a header over the crossbar and Scotland full-back Lee Wallace should have done better than fire straight into the body of McGovern after being put clear behind the Bairns defence.
Rangers' captain also volleyed over from 12 yards following another dangerous corner kick, but neither side was able to display the kind fluency or precision that would set the tie alight.
Falkirk eventually put an effort on target shortly before the break, but former Rangers youth striker Rory Loy's 25-yard drive flew straight into the arms of goalkeeper Cammy Bell.
The Bairns were seen even less as an attacking force after the break even before conceding the penalty, but it took that moment of fragility in the home defence to allow Rangers their first effort on target after the re-start.
Nicky Clark's heel was clipped by McCracken as the striker raced on to a ball behind the Bairns defence, with the central defender being shown a straight red card by referee Brian Colvin.
McCulloch, eyeing a tenth goal of the season, fired his low penalty kick into McGovern's legs and, after Nicky Law volleyed immediately back into the box, the Rangers captain was offside as he flicked the ball into the net.
Rangers went close again when substitute Fraser Aird fired off the underside of the bar and the ball rebounded off the back of defender Kieran Duffie and wide for a corner.
However, Law pounced from 12 yards after an Ian Black free-kick was headed down by Bilel Mohsni then Templeton provided the cool finish from just inside the penatly box after being put clear by Lewis Macleod.
Falkirk manager Gary Holt: "Whether it was or wasn't a sending-off, we'll have to wait and see it again.
"If the referee got it right, he got it right. If he got it wrong, it's part of football.
"We deal with it and move on. David is adamant it wasn't, but I haven't seen it again.
Rangers manager Ally McCoist: "One of the boys at the press conference yesterday said that one of the bookies made us second favourites, which is fair enough.
"But the majority of bookies have still got Aberdeen, Dundee United and Motherwell above us. The bookies don't often get things wrong.
"Time will tell whether we are good enough to beat opposition of that quality, but it's certainly not something that scares us.
"I hope because we scored two late goals that it doesn't take away from the fact that we deserved to win the game.
"I don't think there is any doubt about that. The chances we missed, we could have made life a little bit easier for ourselves."
- 35MillarBooked at 45mins
- 34McCrackenBooked at 57mins
- 33LoySubstituted forShepherdat 82'minutes
- 7FultonSubstituted forAlstonat 73'minutes
- 9RobertsBooked at 42minsSubstituted forFlynnat 60'minutes
- 4PeraltaSubstituted forAirdat 67'minutes
- 7ClarkSubstituted forTempletonat 67'minutesBooked at 90mins
- 18Sanchez Cribari
- Brian Colvin
- Shots on Target
Second Half ends, Falkirk 0, Rangers 2.
David Templeton (Rangers) is shown the yellow card for excessive celebration.
Goal! Falkirk 0, Rangers 2. David Templeton (Rangers) left footed shot from the left side of the box to the bottom right corner.
Attempt missed. Mark Millar (Falkirk) right footed shot from outside the box is too high.
Attempt missed. Mark Millar (Falkirk) right footed shot from more than 35 yards misses to the right.
Goal! Falkirk 0, Rangers 1. Nicky Law (Rangers) left footed shot from the centre of the box to the bottom right corner.
Bilel Mohsni (Rangers) wins a free kick in the defensive half.
Foul by Mark Millar (Falkirk).
Attempt missed. David Templeton (Rangers) right footed shot from outside the box is high and wide to the right.
Attempt missed. Lee McCulloch (Rangers) header from the centre of the box is just a bit too high.
Corner, Rangers. Conceded by Kieran Duffie.
Attempt saved. David Templeton (Rangers) header from the centre of the box is saved in the centre of the goal.
Substitution, Falkirk. Scott Shepherd replaces Rory Loy.
Attempt saved. Lee Wallace (Rangers) right footed shot from outside the box is saved in the centre of the goal.
Attempt saved. Nicky Law (Rangers) right footed shot from the left side of the box is saved in the top centre of the goal.
Corner, Rangers. Conceded by Conor McGrandles.
Corner, Rangers. Conceded by Kieran Duffie.
Lewis MacLeod (Rangers) wins a free kick in the defensive half.
Foul by Kieran Duffie (Falkirk).