Attendance 6,695
The win represents the Ibrox men's most emphatic win at the Falkirk Stadium, where it was a cold, windswept afternoon, as always seems to be case at the new ground on the edge of Grangemouth.
Manager Walter Smith made two changes from Barcelona with Kevin Thomson and Jean-Claude Darcheville replacing Charlie Adam and Brahim Hemdani.
Darcheville almost made an immediate impact, his shot on the turn from an Alan Hutton pass in three minutes being held by home goalkeeper Tim Krul.
Seven minutes later the 'Bairns' somehow survived an almighty scramble in front of their own goal when Darcheville's driven cross was sliced towards his own net by Steven Thomson. Krul somehow clawed the ball out only for Daniel Cousin to bundle the ball back towards the line - but again the goalie kept his charge intact.
The opening goal should certainly have arrived in fourteen minutes when Darcheville's penetrating run took him deep into Falkirk territory before squaring to Barry Ferguson who somehow shot wide with the goal at his mercy.
That was a bad miss - and just to underline that it was not all one-way traffic former Ranger Russell Latapy saw his 25-yard free-kick flash just over three minutes later.
The opening goal duly arrived in twenty minutes when Carlos Cuellar stooped low to head home a DaMarcus Beasley corner.
Conditions were made increasingly difficult by torrential rain as the first-half drew to a close without further scoring.
Referee Charlie Richmond is a controversial figure at the best of times, and he was obviously influenced by the home crowd in the Main Stand when he yellow-carded Beasley ludicrously for alleged simulation when in fact the American had been barged in the back.
Rangers went 2-0 up two minutes later when Lee McCulloch turned Gerard Aafjes wide on the left, his low cross being swept home by Darcheville.
The victory should have been secure, yet once again the idiosyncrasies of Charlie Richmond would influence matters in 61 minutes when he awarded the home side a free-kick ludicrously after Alan Hutton cleanly won the ball in a touchline tackle with substitute Pedro Moutinho.
Dean Holden's free-kick was headed down by Darren Barr, allowing Moutinho to net.
Steven Naismith replaced Cousin nine minutes later, but the 'Bairns' had been reborn by that goal - and it was almost level-pegging in 75 minutes when Graham Barr's overhead-kick from a Moutinho cross was touched over by McGregor.
Five minutes later Boyd replaced Darcheville, but nerves were fraught in Ibrox ranks, underlined when McGregor, at full stretch, turned wide a goalbound Hutton header from an Aafjes cross in 86 minutes.
Rangers nevertheless had weathered the storm - and sealed victory in injury time when McGregor's long throw found Naismith on the halfway line, the striker streaking away down the left before squaring for Boyd to make it 3-1.
FALKIRK Krul; Aafjes, Barr, Milne, Holden; Thomson, Latapy (Moutino 54), Cregg, Arfield; Barrett, Finnigan (Higdon 71) UNUSED SUBS Olejnik, Allison, Riera, Craig, Scobbie tRANGERS McGregor; Hutton, Weir, Cuellar, Papac; Beasley, Ferguson, Thomson, McCulloch; Darcheville (Boyd 80), Cousin (Naismith 70) UNUSED SUBS Carroll, Adam, Whittaker, Lennon, Fleck
REFEREE Charlie Richmond