Rangers 3 Falkirk 1
The Bairns took an early lead through Steve Lovell and it took a soft penalty award just before half-time which was converted by Kris Boyd to draw the Gers level.
Boyd then side-footed home ten minutes from time to put Rangers ahead, before Steve Davis scored in the first minute of injury time to make the points safe.
Both teams had a player sent off with Patrick Cregg red-carded for a bad tackle on Pedro Mendes just after half-time and Sasa Papac for pulling down substitute Mark Stewart on the halfway line.
It was the visitors who dominated early play and Falkirk opened the scoring when Lovell cleverly clipped home a marvellous pass by Neil McCann.
Boyd just failed to reach a superb pass by Barry Ferguson before Kenny Miller delayed too long after Davis created the chance.
Rangers made strong appeals for a penalty when Falkirk keeper Robert Olejnik appeared to catch Boyd on the byline and, after Miller and Mendes both went close, Rangers equalised.
The referee was perhaps influenced by turning down Boyd's earlier claim as it looked a soft award when Rangers top goalscorer went down under Darren Barr's challenge.
Boyd lashed home the resultant spot-kick.
Allan McGregor rescued Rangers at the start of the second half, racing from his goal to deny Lovell.
Falkirk were reduced to ten men when Cregg was sent off for a two-footed tackle on Mendes.
Olejnik saved well from headers from Boyd and Kirk Broadfoot as Rangers tried to take advantage of the extra man.
Twelve minutes from time Papac was sent off for his foul on Stewart but it was Rangers substitute, Nacho Novo, who made the difference with a superb run and cross which the keeper could only palm out to Boyd, who netted from close range.
Falkirk worried Rangers in the last ten minutes before Davis scored after a superb mazy run in the visitors' area.