Rangers 2 Falkirk 0
Until then Rangers led through a goal midway through the first half by Kris Boyd, which was his 15th of the season even though he has spent much of it on the bench.
Falkirk went close on a couple of occasions in the second half but their attack lacked a cutting edge.
The match took a while to come to life with Scott Arfield's volley going narrowly over.
Rangers took the lead after Jean-Claude Darcheville was brought down by Gerard Aafjes on the edge of the penalty area. Boyd drilled his free-kick powerfully through the wall and past keeper Robert Olejnik.
The visitors tried to respond and Aafjes headed Pedro Moutinho's corner over the bar. Carlos Cuellar then tested the Falkirk keeper with a long-range effort which he was happy to parry away.
Darcheville should have put Rangers further ahead when he raced through from halfway but, as he tried to go round the keeper, Olejnik managed to save at his feet.
Boyd was only denied his second just before half-time when Olejnik brilliantly blocked the striker's powerful close-range volley from Chris Burke's corner.
Rangers should have put the game beyond doubt at the start of the second half but Barry Ferguson somehow hooked his shot wide from only four yards after a good break by Brahim Hemdani.
Burke wasted a good run with a poor final pass and Kirk Broadfoot's dangerous cross should have been attacked by either Boyd or Darcheville.
Olejnik again denied Ferguson with a brave block from the skipper's volley after Naismith's early pass had created the chance.
Falkirk nearly spoiled the party near the end. From substitute Russell Latapy's pass, Patrick Cregg went past two defenders before narrowly shooting over.
Naismith finished the game as a contest when he dispossessed Darren Barr on the edge of the box before clinically firing past Olejnik from 18 yards.