Rangers enjoyed the best possible start to the game, opening the scoring after only nine minutes through in-form frontman Kris Boyd.
Pedro Mendes began the move which led to the goal, releasing Nacho Novo on the left. The diminutive Spaniard supplied an inviting low cross which was driven home impressively by the lurking Boyd.
The visitors enjoyed almost total domination throughout the first half, with Mendes looking particularly impressive in midfield.
In the 28th minute the Portuguese star sent a superb cross-field ball to the feet of Steven Davis who in turn played a teasing pass towards the advancing Madjid Bougherra.
However, Falkirk keeper Dani Mallo dived bravely at the feet of the Algerian and averted the danger.
A minute later Novo broke through but became involved in a misunderstanding with team-mate Boyd and the chance disappeared.
Novo again found himself in front of goal eight minutes before the break but on this occasion he was thwarted by a precise tackle from veteran Bairns defender Jackie McNamara.
Falkirk's solitary attempt on goal prior to the interval was a long-range effort from Scott Arfield which was easily held by Rangers keeper Neil Alexander.
The Bairns did, however, begin the second half positively with Kevin McBride, Burton O'Brien and Carl Finnigan all finding themselves in scoring positions but, sadly for the home fans, their respective efforts were weak, as was a tame close-range header from Arfield which was easily collected by Alexander.
Boyd and Mendes both missed chances to increase Rangers' lead towards the end as the Ibrox side held on for victory.