It was a pulsating match from start to finish. Rangers took an early lead when Lee McCulloch's header from Barry Ferguson's corner came back off the bar and David Weir's shot was blocked on the line before Daniel Cousin shot home from six yards.
Steven Whittaker was making his debut and formed a wonderful partnership down the right flank with Alan Hutton.
Falkirk gradually played their way back into the match with Russell Latapy pulling the strings.
A superb quick-passing move by the visitors ended with Pedro Moutinho's chip being brilliantly touched behind by Allan McGregor in the Rangers goal.
The home side increased their lead when Whittaker's shot from Ferguson's pass was deflected past the helpless Tim Krul.
Nacho Novo was denied by Krul's block before Falkirk deservedly reduced the deficit.
Arnau Riera picked up a clearance 25 yards out before unleashing a spectacular shot into the top corner.
Indeed, Falkirk could have been level by half-time but Carlos Cuellar hooked clear a Jack Ross cross from in front of goal.
If the first half had been entertaining, then the second more than matched it as, when Cousin swept home Ferguson's cross, you would have been excused for thinking that Falkirk's resistance was finished.
However, the visitors rallied again when substitute Graham Barrett cleverly chipped over McGregor to give Falkirk some hope of taking something from the match.
But their hopes were dashed when Whittaker's pass released Cousin and, as Krul hesitated, the striker's cross was lashed high into the net by substitute Kris Boyd for his first goal of the season.
Jean-Claude Darcheville came on for the tiring Cousin and, when Boyd's header came back off the post from Whittaker's cross, the French striker was on hand to prod the rebound home.
Darcheville then added a second and Rangers' sixth after Boyd's shot was blocked on the line.
And there was still time for substitute Kirk Broadfoot to score Rangers' seventh after a swift break from the halfway line by Darcheville.