Falkirk 1 Rangers 3
It was hardly a stroll for Rangers as Falkirk pushed them all the way and only goalkeeper Allan McGregor kept his side ahead with two wonderful second-half saves.
Rangers had the best of the opening exchanges and almost grabbed a 10th minute lead when Jean-Claude Darcheville sent a dangerous cross into the box and Falkirk defender Darren Barr almost put the ball into his own net.
However, Tim Krul palmed the ball onto the crossbar and then pushed away the rebound.
Five minutes later, brilliant play from Darcheville set up another chance when he skipped past the Falkirk defence before setting up Barry Ferguson, who broke into the box but somehow shot wide.
Rangers went in front on 20 minutes after a corner won by Alan Hutton was played in by DaMarcus Beasley and fell straight to the head of Carlos Cuellar, who sent a fine looping header past Krul and into the net.
Right at the start of the second half, Falkirk passed up a great chance to equalise when Carl Finnigan pounced on a mistake by Cuellar to go one-on-one with McGregor but, rather than shoot, he crossed into no man's land.
Nine minutes into the second half, Rangers grabbed a second after David Weir sent a long pass to Lee McCulloch who flew down the left before finding the perfect cross for Darcheville to stroke home from close range.
Falkirk grabbed a lifeline in the 62nd minute when substitute Pedro Moutinho cracked a great shot home after Barr had touched a Dean Holden free-kick into his path.
McGregor produced a wonderful save on 75 minutes to push Graham Barrett's terrific overhead kick onto the top of the bar.
With four minutes remaining the keeper was again called into action as he reacted quickly to produce a stunning save to keep out a header that was wayward from team-mate Hutton.
Right on full time, Rangers sealed the points when a long throw out from McGregor found Steven Naismith who rampaged down the line before squaring for Kris Boyd to tap in from close range.